If log104 = 0.6021, evaluate log1041/3

The question is ambiguous as typed, so let me look at the two sensible readings.

Reading 1: log₁₀(4^(1/3))

Use the power rule: log(aⁿ) = n·log a

log₁₀(4^(1/3)) = (1/3) × log₁₀4 = (1/3) × 0.6021 = 0.2007

Reading 2: log₁₀(41/3)

This would be log₁₀41 − log₁₀3. We can't get log₁₀41 from the given value of log₁₀4 alone, so this reading doesn't work. The question must mean 4^(1/3).

Step-by-step solution

1. Rewrite the expression: log₁₀(4^(1/3))
2. Bring the power down: (1/3) × log₁₀4
3. Substitute the given value: (1/3) × 0.6021
4. Calculate: 0.6021 ÷ 3 = 0.2007

Checking the other options

• A (0.3011) is about 0.6021 ÷ 2, which would be log√4, not the cube root.
• B (0.9021) has no logical link to the working.
• C (1.8063) is 3 × 0.6021, which would be log(4³). That is the wrong direction.

Exam tip: In a log question with a fractional power, the power comes out as a multiplier. The exponent 1/3 means "divide by 3", and the exponent 3 means "multiply by 3". Always check which one applies, because options like C are designed to catch students who mix them up.