Question

Which expression is equivalent to log Subscript 2 Baseline 9 x cubed?

Answer 1

a) log2 9x^3

Explanation:

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Answer 2

log Subscript 2 Baseline 9 x cubed is equivalent to 2 log subscript 2 Baseline 3 + 3 log subscript 2 Baseline x

Explanation:

Given:

log Subscript 2 Baseline 9 x cubed?

Required:

Find the equivalent of the above expression.

First, we need to represent it mathematically;

log Subscript 2 Baseline 9 x cubed =
`log_(2) 9x^(3)`

From Laws of logarithm

`log_(x) AB = log_(x) (A* B)\\log_(x) AB = log_(x)A + log_(x)B`

Note how the expression is split into two

We'll apply the same logic above, here

First, is to simplify the mathematical expression;

`log_(2) 9x^(3) = log_(2) (9 * x^(3))`

Then we split into two

`log_(2) 9x^(3) = log_(2)(9) + log_(2)(x^(3))`

`log_(2) 9x^(3) = log_(2)(3^2) + log_(2)(x^(3))`

Also from laws of logarithm,

`log_(m)A^(n) = nlog_(m)A`

We'll apply this law on
`log_(2)(x^(3))` and
`log_(2)(3^(2))`

`log_(2)x^(3) = 3log_(2)x`

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

So,
`log_(2) 9x^(3) = log_(2)(9) + log_(2)(x^(3))` becomes

`log_(2) 9x^(3) = 2log_(2)3 + 3log_(2)x`

log Subscript 2 Baseline 9 x cubed is equivalent to
`2log_(2)3 + 3log_(2)x`

`2log_(2)3` can be represented as 2 log subscript 2 Baseline 3

and

`3log_(2)x` can be represented as 3 log subscript 2 Baseline x

Hence, log Subscript 2 Baseline 9 x cubed is equivalent to 2 log subscript 2 Baseline 3 + 3 log subscript 2 Baseline x