Question

Which of the following is equivalent to log168?

2



1.248



4 over 3



3 over 4

Answer 1

Hello there.

Which of the following is equivalent to log168?

3 over 4

Answer 2

Option (d) is correct.

The value of given expression
`log_{\left\{16\right\}}8` is
`(3)/(4)`

Explanation:

Given : expression
`log_{\left\{16\right\}}8`

We have to evaluate the value of given expression
`log_{\left\{16\right\}}8`

Consider the given expression
`log_{\left\{16\right\}}8`

Rewrite 16 as power- base form as
`2^4`

Apply log rule ,
`\log _(a^b)\left(x\right)=(1)/(b)\log _a\left(x\right)`

We have,

`\log _(2^4)\left(8\right)=(1)/(4)\log _2\left(8\right)`

Simplify, we have,

`=(1)/(4)\log _2\left(8\right)`

Rewrite 8 as power- base form as
`2^3`

`=(1)/(4)\log _2\left(2^3\right)`

Apply log rule,
`\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)`

We have,

`\log _2\left(2^3\right)=3\log _2\left(2\right)`

Apply log rule,
`\log _a\left(a\right)=1`

We have,

`(1)/(4)\cdot \:3\cdot \:1=(3)/(4)`

Thus, The value of given expression
`log_{\left\{16\right\}}8` is
`(3)/(4)`