Question

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

Answer 1

Answer:

a) log2 9x^3

Step-by-step explanation:

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Answer 2

Answer:

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

Step-by-step 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