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Black Lotus · Answer 1 · 2023-05-25T01:16:32+0000

we have the system of equations

$\begin{gathered} f(x)=\log_2x+2 \\ g(x)=\log_2x^3-6 \end{gathered}$

Equate the functions f(x) and g(x)

$\log_2x+2=\log_2x^3-6$

Apply property of logarithms

$\begin{gathered} \operatorname{\log}_2x+2=3\operatorname{\log}_2x-6 \\ 3\operatorname{\log}_2x-\operatorname{\log}_2x=2+6 \\ 2\operatorname{\log}_2x=8 \\ \operatorname{\log}_2x=4 \end{gathered}$

Apply the definition of logarithm

$\begin{gathered} 2^4=x \\ x=16 \end{gathered}$

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