Question

simplify the product into a quotient of natural logarithms. \\(\log_{3}(6) \cdot \log_{6}(5)\\) question help: \\(\boldsymbol{}\\) message instructor

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:

$\frac{\ln(5)}{\ln(3)}$