If $\left[\left(10^{3}\right)\left(10^{x}\right)\right]^{2}=10^{18}$, the value of $x$ is
(A) $\sqrt{2}$
(B) 12
(C) 6
(D) 1
(E) 3
If $\left[\left(10^{3}\right)\left(10^{x}\right)\right]^{2}=10^{18}$, the value of $x$ is
(A) $\sqrt{2}$
(B) 12
(C) 6
(D) 1
(E) 3

## Solution

If we simplify using laws of exponents, we will have,

$$
\begin{gathered}
\left(10^{3+x}\right)^{2}=10^{18} \\
10^{6+2 x}=10^{18}
\end{gathered}
$$

In order that the left and right side be equal, it is necessary that exponents be equal.

$$
\text { Thus, } \begin{aligned}
6+2 x & =18 \\
2 x & =12 \\
x & =6 .
\end{aligned}
$$

ANSWER: (C)