Question

What is log15 2^3 rewritten using the power property?

Answer 1

The required expression is
`3\log_(15)2`.

Explanation:

According to the power property of exponent,

`\log_ax^b=b\log_ax`

The given expression is

`\log_(15)2^3`

Here a=15, x=2, b=3.

Using power property of exponent the given expression can be written as

`\log_(15)2^3=3\log_(15)2`

Therefore the required expression is
`3\log_(15)2`.

Answer 2

`log_(15)( {2}^(3) ) = 3 \: log_(15)( {2} )`

EXPLANATION

According to the power property of logarithms:

`log_(x)( {y}^(n) ) = n \: log_(x)( {y} )`

The given logarithm is

`log_(15)( {2}^(3) )`

When we apply the power property to this logarithm, we get,

`log_(15)( {2}^(3) ) = 3 \: log_(15)( {2} )`