How do you evaluate ${log}_{5} (\frac{1}{2})$ $log_5(1/2)$ ?

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Answer 1 · 2016-05-02T19:21:53

By calculator -0.431 (3 dec places)

Let ${log}_{5} (\frac{1}{2}) = x$ $log_5 (1/2) = x$

Change from log form to index from: $5^{x} = \frac{1}{2}$ $5^x = 1/2$

Now, because the variable is the index, and $\frac{1}{2}$ $1/2$ is not an exact power of 5, we need to use logs.

Power law: $x log 5$ $x log5$ = log 0.5)

$x = \frac{log 0.5}{log 5}$ $x = (log0.5)/(log5)$

From a calculator $x$ $x$ = -0.431

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