Solve the Logarithmic Equation: 3log₇6 Step by Step

To simplify the expression $3\log_76$, we apply the power property of logarithms, which states:

$a\log_b c = \log_b(c^a)$

Step 1: Identify the given expression: $3\log_76$.

Step 2: Apply the power property of logarithms:

$3\log_76 = \log_7(6^3)$

Step 3: Calculate $6^3$:

$6^3 = 6 \times 6 \times 6 = 36 \times 6 = 216$

Step 4: Substitute back into the logarithmic expression:

$\log_7(6^3) = \log_7216$

Therefore, the simplified expression is $\log_7216$.

Comparing with the answer choices, the correct choice is:

$\log_7216$