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Evaluate the expression log 9(0.3). Please round your answer to the nearest ten-thousandth.

User Awaken
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Final answer:

To evaluate the expression log 9(0.3), we can use the change of base formula to convert it to the common logarithm. Using a calculator, we find that log 9(0.3) ≈ -0.5487.

Step-by-step explanation:

The expression log9(0.3) represents the logarithm of 0.3 with base 9. To evaluate this expression, we can use the change of base formula, which states that logab = logcb / logca. Let's use the common logarithm (base 10) as the new base:

log9(0.3) = log10(0.3) / log10(9)

Using a calculator, we find that log10(0.3) ≈ -0.5229 and log10(9) ≈ 0.9542. Therefore, log9(0.3) ≈ -0.5229 / 0.9542 ≈ -0.5487.

User Yellowsir
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