Source: Extra Practice
Find the value of the expression: 1/log₃(30) + 1/log₂(30) + 1/log₅(30).
Options
Option A is correct
1
Option B
0
Option C
log₁₀(30)
Option D
30
Explanation
This question utilizes the base change property: 1/logₐ(b) = log_b(a). Applying this to each term, the expression becomes log₃₀(3) + log₃₀(2) + log₃₀(5). Using the product rule of logarithms (logₐ(m) + logₐ(n) + logₐ(p) = logₐ(mnp)), we combine the terms: log₃₀(3 * 2 * 5) = log₃₀(30). Since any logarithm where the base and the argument are the same (logₐ(a)) equals 1, the final value is 1. Options 0 and 30 are mathematically inconsistent with these logarithmic identities.