Question

Which expression is equivalent to log Subscript 2 Baseline 9 x cubed? log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x log Subscript 2 Baseline x + 3 log Subscript 2 Baseline 9 3 log Subscript 2 Baseline x minus log Subscript 2 Baseline 9 3 log Subscript 2 Baseline 9 minus log Subscript 2 Baseline x

Answer 1

Answer:

log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x.

Log₂ 9 + 3Log₂ x

Step-by-step explanation:

Log subscript 2 baseline 9 x cubed can be written as:

Log₂ 9x³

Now, let us simply Log₂ 9x³.

This is illustrated below:

Log₂ 9x³

Recall: LogMN = Log M + Log N

Log₂ 9x³ = Log₂ 9 + Log₂ x³

Recall: Log Mⁿ = nLog M

Log₂ 9x³ = Log₂ 9 + 3Log₂ x

Therefore, the answer is log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x.

Answer 2

The equivalent expression of $\log_2(9x^3)$ is $\log_2(9) + 3\log_2(x)$

The logarithmic expression is given as:

$\log_2(9x^3)$

Apply the quotient law of logarithm

$\log_2(9x^3) = \log_2(9) + \log_2(x^3)$

Apply the power rule of logarithm

$\log_2(9x^3) = \log_2(9) + 3\log_2(x)$

Hence, the equivalent expression of $\log_2(9x^3)$ is $\log_2(9) + 3\log_2(x)$

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