1. ## Logs

Determine value of the expression 1/logbase9(15) + 1/logbase25(15)

2. First add the fractions, then use the change of base formula $\displaystyle log_bx=\frac{log_ax}{log_ab}$

3. Originally Posted by Tiger
Determine value of the expression 1/logbase9(15) + 1/logbase25(15)
Use the change of base rule: $\displaystyle log_c(a) = \frac{log_b(a)}{log_b(c)}$

$\displaystyle log_{9}(15) = \frac{ln(15)}{ln(9)}$

$\displaystyle log_{25}(15) = \frac{ln(15)}{ln(25)}$

Flipping the two results above and adding gives: $\displaystyle \frac{ln(25)+ln(9)}{ln(15)}$

Simplify using the log multiplication rule: $\displaystyle a\,ln(k) = ln(k^a)$

$\displaystyle \frac{ln(25)+ln(9)}{ln(15)} = \frac{2[ln(5)+ln(3)]}{ln(15)}$

Simplify using the log addition rules: $\displaystyle ln(a)+ln(b) = ln(ab)$

$\displaystyle \frac{2[ln(5)+ln(3)]}{ln(15)} = \frac{2ln(15)}{ln(15)} = 2$