{"id":6399,"date":"2021-12-21T12:49:29","date_gmt":"2021-12-21T12:49:29","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6399"},"modified":"2022-01-03T07:38:56","modified_gmt":"2022-01-03T07:38:56","slug":"how-to-use-log-table-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/how-to-use-log-table-examples\/","title":{"rendered":"How to use log table \u2013 Examples"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
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How to use log table \u2013 Examples <\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

How to use log table\u00a0<\/b><\/h2>\n

A logarithm is the inverse of the exponential function.<\/span><\/p>\n

a^{b}=\\text{x} <\/span>
\u21d2 \\log _{a} {\\text x}=b<\/span><\/p>\n

Here, the logarithm of x with base a is equal to b.<\/span><\/p>\n

It is mainly classified into 3 types based on the value of the base.<\/span><\/p>\n

Common logarithm of \\text{x}=\\log _{10} \\text{x}(\\text { Base }=10)<\/span><\/span><\/p>\n

Natural logarithm of \\text{x}=\\log _{e} \\text{x}(\\text { Base }=e)<\/span><\/span><\/p>\n

Binary logarithm of \\text{x}=\\log _{2} \\text{x}(\\text { Base }=2)<\/span><\/span><\/p>\n

<\/span><\/p>\n

Logarithm of x = Characteristic of x + Mantissa of x<\/strong><\/p>\n

Characteristic is an integer whereas mantissa is a decimal number.<\/span><\/p>\n

 <\/p>\n

Finding Characteristic of x<\/b><\/h2>\n

1. Write the number in scientific form.<\/span><\/b><\/p>\n

For example, \\left(15.53=1.553 \\times 10^{1}\\right) \\text { and }\\left(0.0045=4.5 \\times 10^{-3}\\right)<\/span><\/span><\/b><\/span><\/b><\/p>\n

<\/span><\/p>\n

2. The power of base is the characteristic of x.<\/span><\/p>\n

<\/span><\/p>\n

Finding the Mantissa of x<\/b><\/h2>\n

1. Different log tables are used for common logarithm and Natural logarithm depending on the base of the logarithm.<\/span><\/p>\n

<\/span><\/p>\n

2. Search for the row number corresponding to the first two digits of x.<\/span><\/p>\n

Search for the column number corresponding to the third digit of x.<\/span><\/p>\n

Note the value at the intersection of the row and column given above.<\/span><\/p>\n

<\/span><\/p>\n

3. Search for the row number corresponding to the first two digits of x.<\/span><\/p>\n

Search for the row number corresponding to the fourth digit of x on the mean difference table.<\/span><\/p>\n

Note the value at the intersection of the row and column given above.<\/span><\/p>\n

<\/span><\/p>\n

4. Add the values obtained in step 2 and step 3 to obtain the mantissa.<\/span><\/p>\n

<\/span><\/p>\n

Finding the value of the logarithm<\/b><\/b><\/h2>\n

Logarithm of x = Characteristic of x + Mantissa of x<\/strong><\/p>\n

<\/strong><\/p>\n

\"\"<\/span><\/p>\n

<\/span><\/p>\n

Solved Examples<\/b><\/h2>\n

<\/b><\/p>\n

1. Find the value of \\log _{10} 15.53<\/span>.<\/h3>\n

Solution:<\/h3>\n

Finding Characteristic\u00a0<\/strong><\/p>\n

Write the number in scientific form.<\/span><\/p>\n15.53=1.553 \\times 10^{1}<\/span>\n

The power of base is the characteristic.\u00a0<\/span><\/p>\n

Here the base is 10 and the power of 10 is 1. Hence,1 is the characteristic.<\/span><\/p>\n

<\/span><\/p>\n

Finding the Mantissa\u00a0<\/strong><\/p>\n

1. Different log tables are used for common logarithm and Natural logarithm depending on the base of the logarithm. We have to refer to the common logarithm table as the base is 10.<\/span><\/p>\n

2. Search for the row number corresponding to the first two digits 15.<\/span><\/p>\n

Search for the column number corresponding to the third digit of 5.<\/span><\/p>\n

Note the value at the intersection of row 15 and column 5.<\/span><\/p>\n

The value is 1903.<\/span><\/p>\n

3. Search for the row number corresponding to the first two digits 15.<\/span><\/p>\n

Search for the row number corresponding to the fourth digit 3 on the mean difference table.<\/span><\/p>\n

Note the value at the intersection of row 15 and column 3 of the mean difference table.\u00a0<\/span><\/p>\n

The value is 8.<\/span><\/p>\n

4. Add the values obtained in step 2 and step 3 to obtain the mantissa.<\/span><\/p>\n

1903 + 8 = 1911<\/span><\/p>\n

Hence the mantissa of 15.53 is 0.1911.<\/span><\/p>\n

\u00a0<\/span><\/p>\n

Value of the logarithm<\/strong><\/p>\n

Logarithm of x = Characteristic of x + Mantissa of x<\/span><\/p>\n

\\log _{10} 15.53=1+0.1911=1.1911<\/span><\/span><\/p>\n

<\/span><\/p>\n

2. Find the value of \\log _{10} 0.243<\/span>.<\/span><\/h3>\n

Solution:<\/span><\/h3>\n

Finding Characteristic<\/strong>\u00a0<\/span><\/p>\n

Write the number in scientific form.<\/span><\/p>\n

0.243=2.43 \\times 10^{-1}<\/span><\/span><\/p>\n

The power of base is the characteristic\u00a0<\/span><\/p>\n

Here the base is 10 and the power of 10 is -1. Hence, (-1) is the characteristic.<\/span><\/p>\n

<\/span><\/p>\n

Finding the Mantissa\u00a0<\/strong><\/p>\n

1. Different log tables are used for common logarithm and Natural logarithm depending on the base of the logarithm. We have to refer to the common logarithm table as the base is 10.<\/span><\/p>\n

2. Search for the row number corresponding to the first two digits 24.<\/span><\/p>\n

Search for the column number corresponding to the third digit of 3.<\/span><\/p>\n

Note the value at the intersection of row 24 and column 3.<\/span><\/p>\n

The value is 3856.<\/span><\/p>\n

There is no fourth digit. So we have to stop here.<\/span><\/p>\n

Hence the mantissa of 0.243 is 0.3856.<\/span><\/p>\n

<\/span><\/p>\n

Value of the logarithm<\/strong><\/p>\n

Logarithm of x = Characteristic of x + Mantissa of x<\/span><\/p>\n

\\log _{10} 0.243=(-1)+0.3856=(-0.6144)<\/span><\/span><\/p>\n

<\/span><\/p>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\n

Explore Other Topics<\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n

\n
Geometry<\/a><\/div>\n
Trigonometry<\/a><\/div>\n
Operations<\/a><\/div>\n
Numbers<\/a><\/div>\n<\/div>\n

[\/et_pb_text][et_pb_text admin_label=”Related Concepts
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\n

Related Concepts<\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n

\n
Value of log 0<\/a><\/div>\n
Exponential form<\/a><\/a><\/div>\n<\/div>\n

[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.10.6″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” admin_label=”Image” module_class=”img1″ _builder_version=”4.10.8″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n

\n
\n
\n

Ready to get started ?<\/p>\n<\/div>\n

\n

Start Free Trial<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n

[\/et_pb_text][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/down-circle.png” title_text=”down-circle” show_bottom_space=”off” align=”right” module_class=”img2″ _builder_version=”4.9.10″ _module_preset=”default” width=”44px” height=”18px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”FAQ Row” _builder_version=”4.9.11″ _module_preset=”default” width=”100%” max_width=”1310px” custom_padding=”|40px||40px|false|true” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”FAQ” module_class=”faqstyl” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_font=”|700|||||||” header_text_align=”center” header_line_height=”2.5em” background_color=”#dbedc6″ max_width=”80%” module_alignment=”center” custom_margin=”||||false|false” custom_padding=”30px|25px|30px|25px|true|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”]<\/p>\n

<\/h1>\n

Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
    <\/ol>\n

    Q1. How many types of logarithm are there?
    <\/strong><\/h3>\n

    Ans: <\/strong>There are three types of logarithm classified on the basis of base.
    <\/span><\/p>\n

      \n
    • Common logarithm of x =\\log _{10} \\text{x}(\\text { Base }=10)<\/span><\/span><\/li>\n
    • Natural logarithm of x =\\log _{e} \\text{x}(\\text { Base }=\\mathrm{e})<\/span><\/span><\/li>\n
    • Binary logarithm of x =\\log _{2} \\text{x}(\\text { Base }=2)<\/span><\/span><\/li>\n<\/ul>\n

      Q2. What is a log table?<\/strong><\/span><\/p>\n

      Ans: <\/strong>It is the table used for finding out the value of any logarithm.<\/p>\n

      Q3. What is the logarithm of a number?
      <\/strong><\/p>\n

      Ans:\u00a0 <\/strong>It is the inverse of the exponential function<\/span><\/p>\n

      \u00a0 \u00a0 a^{b}=x <\/span>
      \u21d2\\log _{a} x=b<\/span><\/span><\/p>\n

      Here logarithm of x with base a is equal to b.<\/span><\/p>\n

      [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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