Question

Use the change of base formula to evaluate the expression then convert it to a logarithm in base eight round to the nearest thousandth

Answer 1

Recall that the change of base formula for logarithms is:

$\log_a(b)=\frac{\log_x(b)}{\log_x(a)}.$

Using the change of base formula for logarithms to the given logarithm we get:

$\log_354=\frac{\log_8(54)}{\log_8(3)}.$

Therefore:

$\log_3(54)=3.631.$

And:

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