Question

Find the value of log8/log root 2

Answer 1

Given,

A trigonometric expression log8/log√2.

To Find,

The value of this trigonometric expression.

Solution,

The given expression is log8/log√2 which can also be written as

log8 = log 2³ = 3 log2 { logmⁿ = n logm}

Also,

log√2 = log2^1/2 = 1/2 log2

Now,

log8/log√2 = 3 log2/(1/2 log2)

log8/log√2 = 3*2 log2/log2

log8/log√2 = 6

Hence, the value of log8/log√2 is 6.

Answer 2

Given:

log8/log root 2

To find:

The value of log8/log root 2

Solution:

The required value is 6.

We can solve the numerator and denominator separately and then divide to obtain the value.

log8= log $2^{3}$

log root 2= log $2^{1/2}$

We know that $log a^{b}$ = b log a.

Using this,

log8=3 log 2

log√2=1/2 log 2

The required value=log8/ log√2

=3 log 2/1/2 log 2

=3/ (1/2)

=3×2

=6

Therefore, the required value is 6.