Question

If ${\left(2^3\right)}^2=4^x$, then $3^x=$

• A. a) $6$
• B. b) $9$
• C. c) $27$
• D. d) $3$

Answer 1

The correct option is C

c) $27$

Option (c): $27$

Step 1 : Find the value of $x$

Given that ${\left(2^3\right)}^2=4^x$.

To find the value of $3^x$ we need to find the value of $x$ first.

$$\begin{gathered} {\left(2^3\right)}^2=4^x \\ {\left(2^3\right)}^2={\left(2^2\right)}^x[\because 4=2\times 2=2^2] \\ {2}^6=2^{2x}[\because {\left(a^m\right)}^n=a^{mn}] \\ 6=2x[If{a}^x=a^y,thenx=y] \\ x=\frac{6}{2} \\ x=3 \end{gathered}$$

Step 2 : Find the value of $3^x$

Now, putting the value of $x$ in $3^x$, we get

$\Rightarrow 3^x=3^3=27$.

Therefore, the value of $3^x$ is $27$.

Hence, the correct answer is option $\left(C\right)$.