Question

algebra: concepts and connections - plc solving exponential equations by rewriting the base if $3^{2x + 1} = 3^{x + 5}$, what is the value of $x$? options: 4, 2, 6, 3

Explanation:

Step1: Set exponents equal (same base)

Since the base $3$ is non-zero and not equal to $1$, we can equate the exponents:
$2x + 1 = x + 5$

Step2: Isolate $x$ (subtract $x$)

Subtract $x$ from both sides:
$2x - x + 1 = 5$
$x + 1 = 5$

Step3: Solve for $x$ (subtract 1)

Subtract 1 from both sides:
$x = 5 - 1$

Answer:

4