1 Answer

Brewal · Answer 1 · 2023-07-03T10:15:05+0000

Answer:

A. The solution set is {4096}.

Explanation:

Given the logarithmic equation:

$(1)/(2) \log _(6) x=3 \log _(6) 4$

Multiply both sides of the equation by 2:

$\begin{gathered} (1)/(2)*2\log_6x=3*2\log_64 \\ \log_6x=6\log_64 \end{gathered}$

Next, apply the power law of logarithms to the right side of the equation.

$\begin{gathered} \log_6x=\log_64^6 \\ \implies\operatorname{\log}_6x=\operatorname{\log}_64096 \end{gathered}$

Since the bases are the same, equate the numbers:

The solution set is {4096}.

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