Question

solve plzzzzzzzz.. ​

Answer 1

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

The required answer is 2.

$\rule{200}4$

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

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

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.

Answer 2

Answer:

Formula:

logb(x) = y, if by = x

Input:

x = 4096

b = 8

$\mathbb\orange{SOLUTION}$

y = log₈4096

= log₈ 8⁴

= 4 log₈8 = 4 x 1

log₈4096 = 4

$\huge\mathfrak \pink{hope \: this \: helps \: u}$