simplify the product into a quotient of natural logarithms. \\(\\log_{3}(6) \\cdot \\log_{6}(5)\\) question…
simplify the product into a quotient of natural logarithms. \\(\\log_{3}(6) \\cdot \\log_{6}(5)\\) question help: \\(\\boldsymbol{}\\) message instructor
Answer
Explanation:
Step1: Apply change of base formula
$\log_{3}(6) = \frac{\ln(6)}{\ln(3)}$, $\log_{6}(5) = \frac{\ln(5)}{\ln(6)}$
Step2: Multiply the two expressions
$\frac{\ln(6)}{\ln(3)} \cdot \frac{\ln(5)}{\ln(6)}$
Step3: Cancel common terms
$\frac{\ln(5)}{\ln(3)}$
Answer:
$\frac{\ln(5)}{\ln(3)}$