Question

if $3^x \times 3^x \times 3^x \times 3^x = 9$, which of the following could be the value of $x$?\
(a) $\frac{1}{2}$\
(b) $\frac{1}{4}$\
(c) $0$\
(d) $-\frac{1}{3}$\
(e) $-\frac{1}{2}$

Explanation:

Step1: Combine left-hand side terms

When multiplying exponents with the same base, add exponents:
$3^x \times 3^x \times 3^x \times 3^x = 3^{x+x+x+x} = 3^{4x}$

Step2: Rewrite right-hand side as base 3

$9 = 3^2$, so the equation becomes:
$3^{4x} = 3^2$

Step3: Equate exponents and solve

Since bases are equal, set exponents equal:
$4x = 2$
$x = \frac{2}{4} = \frac{1}{2}$

Answer:

(A) $\frac{1}{2}$