if $3^x \\times 3^x \\times 3^x \\times 3^x = 9$, which of the following could be the value of $x$?\\n(a)…

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

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

Answer

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) $\frac{1}{2}$