`log_b (root(3)(3b))` Approximate the logarithm using the properties of logarithms, given `log_b (2) ~~ 0.3562, log_b (3) ~~ 0.5646, and log_b (5) ~~ 0.8271`.

Textbook Question

Chapter 3, 3.3 - Problem 66 - Precalculus (3rd Edition, Ron Larson).
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balajia | College Teacher | (Level 1) eNoter

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`log_b((3b)^(1/3))=(1/3)log_b(3b)`

`=(1/3)log_b(3)+(1/3)log_b(b)`

`=(1/3)(0.5646+1)`

=(1.5646/3)

=0.5215

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