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If 3^x=81, then x^3=
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23 Sep 2025, 01:09
23 Sep 2025, 01:09
Expert Reply
00:00
Question Stats:
100% (00:28) correct
0% (00:00) wrong based on 13 sessions
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If $\(3^x=81\)$, then $\(x^3=\)$
(A) 12
(B) 16
(C) 64
(D) 81
(E) 128
(A) 12
(B) 16
(C) 64
(D) 81
(E) 128
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- Also replying to the unanswered questions
Re: If 3^x=81, then x^3=
[#permalink]
15 Oct 2025, 22:49
15 Oct 2025, 22:49
Expert Reply
The question asks for the value of $\(x^3\)$ given the equation $\(3^x=81\)$.
Step 1: Find the value of $x$
The given equation is:
$$
\(3^x=81\)
$$
To solve for $x$, express 81 as a power of 3 .
$$
\(81=3 \times 3 \times 3 \times 3=3^4\)
$$
Substitute this back into the equation:
$$
\(3^x=3^4\)
$$
Since the bases are the same (and greater than 1 ), the exponents must be equal:
$$
\(x=4\)
$$
Step 2: Calculate $\(x^3\)$
Now substitute the value of $x=4$ into the expression $\(x^3\)$ :
$$
\(x^3=4^3\)
$$
Calculate $\(4{ }^3\)$ :
$$
\(\begin{gathered}
4^3=4 \times 4 \times 4 \\
4 \times 4=16 \\
16 \times 4=64
\end{gathered}\)
$$
Therefore, $\(x^3=64\)$.
Conclusion
The value of $\(x^3\)$ is $\(\mathbf{6 4}\)$. This corresponds to option (C).
Step 1: Find the value of $x$
The given equation is:
$$
\(3^x=81\)
$$
To solve for $x$, express 81 as a power of 3 .
$$
\(81=3 \times 3 \times 3 \times 3=3^4\)
$$
Substitute this back into the equation:
$$
\(3^x=3^4\)
$$
Since the bases are the same (and greater than 1 ), the exponents must be equal:
$$
\(x=4\)
$$
Step 2: Calculate $\(x^3\)$
Now substitute the value of $x=4$ into the expression $\(x^3\)$ :
$$
\(x^3=4^3\)
$$
Calculate $\(4{ }^3\)$ :
$$
\(\begin{gathered}
4^3=4 \times 4 \times 4 \\
4 \times 4=16 \\
16 \times 4=64
\end{gathered}\)
$$
Therefore, $\(x^3=64\)$.
Conclusion
The value of $\(x^3\)$ is $\(\mathbf{6 4}\)$. This corresponds to option (C).
gmatclubot
Re: If 3^x=81, then x^3= [#permalink]
15 Oct 2025, 22:49
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