Solve 2log₃8: Step-by-Step Logarithm Equation Solution

$2\log_38=$

To solve this problem, let's simplify $2\log_3 8$ using logarithm rules.

• Step 1: Recognize the expression form
  The expression is of the form $a \cdot \log_b c$, where $a = 2$, $b = 3$, and $c = 8$.
• Step 2: Apply the power property
  According to the power property of logarithms, $2 \cdot \log_3 8$ can be simplified to $\log_3 (8^2)$.
• Perform the calculation
  Calculate $8^2$, which is $64$.
• Step 3: Simplify further
  Therefore, we have $\log_3 64$.

This is a straightforward application of the power property of logarithms. By applying this property correctly, we've simplified the original expression correctly.

Therefore, the simplified form of $2\log_3 8$ is $\log_3 64$.