Theory question 101
Logarithms(b) Evaluate log5(3/5) + 3log5(15/2) − log5(81/8)
Show the model answer
Model answer
Combine: log5[3/5 × (15/2)3 ÷ 81/8] = log5[3/5 × 3375/8 × 8/81].
3 × 3375/(5 × 81) = 10125/405 = 25.
log525 = log552 = 2.
Explanation
Turn the coefficient 3 into a power first, then combine into a single log.