Question

Find the value of
log8√4096
​

Answer 1

$\large{\underline{\underline{\red{\bf{Answer:}}}}}$

• The required answer is 2.

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$\large{\underline{\underline{\red{\bf{Step\:by\:step\: explanation:}}}}}$

${\underline{\underline{\purple{\bf{Given:}}}}}$

• A logarithm is given to us.
• The logarithm is $\sf{log_{8}^{\sqrt{4096}}}$

${\underline{\underline{\purple{\bf{To\: Find:}}}}}$

• The value of the given logarithm.

${\underline{\underline{\purple{\bf{Answer:}}}}}$

Taking the given logarithm ,

= $\sf{log_{8}^{\sqrt{4096}}}$

= $\sf{ log_{8}^{\sqrt{64\times 64}}}$

= $\sf{log _{8} ^{64}}$

= $\sf{log _{8} ^{8^2}}$

= $\sf{2\times log_{8}^{8}}$

= $\sf{2\times1}$

=$\bf{2}$

Hence the required answer is 2.

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${\underline{\underline{\purple{\bf{Some\:more\: information:}}}}}$

There are two systems of logarithm ,

• Natural logarithm
• Common logarithm

${\orange{\bf{\leadsto Natural \: logarithms:}}}$

• These were introduced by Napier. They are calculated to the base e (Euler's number) , whose value is approximately equal to 2.7828. These are used in higher mathematics .

${\orange{\bf{\leadsto Common \: logarithms:}}}$

• The logarithms to the base 10 are called Common logarithms . This was introduced by Briggs , who was contemporary of Napier .

${\underline{\underline{\purple{\bf{\longmapsto Properties\:of\: logarithms:}}}}}$

• Logs are defined for positive bases only. (except 1).
• It is defined for positive real numbers.