Question

For any positive number b not equal to 1 and any number or variable n, evaluate the following expression

b^{log_{b}n } =

A. n
B. Log b
C. Log n
D. b

Answer 1

The answer to this question is

A.n

Answer 2

`b^{\log_(b)n }=n`

Explanation:

we are given

`b^{\log_(b)n }`

Let
`b^{\log_(b)n } =y`

`y= b^{\log_(b)n }`

taking log on both hand sides

`\log y = \log (b^{\log_(b)n })`

`\log y = {\log_(b)n} \log b`

`{\log_(b)n}=(\log n)/(\log b)`

`\log y=(\log n)/(\log b)* \log b`

`\log y = \log n`

`y=n`

Hence our expression is equal to n