in which of the options below does x = 5? select all that apply. a) $2^x = 32$ b) $left(\\frac{4}{x}\\right)^…

in which of the options below does x = 5? select all that apply. a) $2^x = 32$ b) $left(\\frac{4}{x}\\right)^2 = \\frac{16}{25}$ c) $x^3 = 125$ d) $left(\\frac{1}{x}\\right)^2 = \\frac{1}{36}$

in which of the options below does x = 5? select all that apply. a) $2^x = 32$ b) $left(\\frac{4}{x}\\right)^2 = \\frac{16}{25}$ c) $x^3 = 125$ d) $left(\\frac{1}{x}\\right)^2 = \\frac{1}{36}$

Answer

Answer:

A) $2^x = 32$, B) $\left(\frac{4}{x}\right)^2 = \frac{16}{25}$, C) $x^3 = 125$

Explanation:

Step1: Check Option A

Rewrite 32 as $2^5$, so $2^x=2^5$. Equate exponents: $x=5$.

Step2: Check Option B

Take square root: $\frac{4}{x}=\pm\frac{4}{5}$. For $\frac{4}{x}=\frac{4}{5}$, solve: $x=5$.

Step3: Check Option C

Rewrite 125 as $5^3$, so $x^3=5^3$. Equate bases: $x=5$.

Step4: Check Option D

Take square root: $\frac{1}{x}=\pm\frac{1}{6}$. Solve: $x=6$ or $x=-6$, not 5.