Use the change of base formula to approximate the value of log 6 21 to the nearest ten thousandths place.
Let x = log_6(21). Then
6^x = 6^(log_6(21)) = 21
log_10(6^x) = log_10(21)
x log_10(6) = log_10(21)
x = log_10(21)/log_10(6)
≈ 1.699180325
= 1.6992 to the nearest ten-thousandths place.
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Verified answer
Let x = log_6(21). Then
6^x = 6^(log_6(21)) = 21
log_10(6^x) = log_10(21)
x log_10(6) = log_10(21)
x = log_10(21)/log_10(6)
≈ 1.699180325
= 1.6992 to the nearest ten-thousandths place.