Evaluate 1/log₃ 60 + 1/log₄ 60 + 1/log₅ 60.

Given data

• Expression: 1/log₃60 + 1/log₄60 + 1/log₅60

Concept / Approach

• Use change-of-base: 1/log_ba = log_ab.
• Combine logs with the same base by converting all to base 60.

Step-by-step calculation

1/log₃60 = log₆₀31/log₄60 = log₆₀41/log₅60 = log₆₀5Sum = log₆₀3 + log₆₀4 + log₆₀5 = log₆₀(3 × 4 × 5)= log₆₀60 = 1

Verification

Since 3 × 4 × 5 equals 60 exactly, the log base 60 of 60 is 1.

Common pitfalls

• Adding denominators directly instead of transforming with change-of-base.
• Using natural logs without keeping bases consistent.

Final Answer

1