Question

fund value if log base under root 4/3 of 64/27

Answer 1

Given,

$log_{\sqrt{\frac{4}{3} }}(\frac{64}{27} )$

To find,

The value of :-

$log_{ \sqrt{ \frac{4}{3} }}(\frac{64}{27} )$

Main solution :-

$log_{ \sqrt{ \frac{4}{3} } } {( \frac{4}{3} )}^{3}$

We know,

log m^n = n log m

This is called power law of logarithms.

Using this law , we get :-

$3 log_{ \sqrt{ \frac{4}{3} } }( \frac{4}{3} )$

We know that (4/3) can be written as (√(4/3))^2

Using this , we get :-

$3 log_{ \sqrt{ \frac{4}{3} } }( \sqrt{ \frac{4}{3} } )^{2}$

Now again using power law , we get :-

$6log_{\sqrt{ \frac{4}{3} } }( \sqrt{ \frac{4}{3} } )$

We know, log m to the base m = 1.

It is the similar case here as base and the value is same.

We get :-

$6\times1$

$6$

Answer :- 6