How do you evaluate $f (x) = {log}_{16} x$ $f(x)=log_16x$ for x=4?

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Answer 1 · 2017-08-01T04:42:50

${log}_{16} (4) = \frac{1}{2}$ $log_16(4) = color(blue)(1/2$

We're asked to evaluate

${log}_{16} (4)$ $log_16(4)$

This can also be written as

$16^{x} = 4$ $16^x = 4$

We know that $4$ $4$ is the square root of $16$ $16$ , so

$4 = 16^{1 / 2}$ $4 = 16^(1"/"2)$

(which is equivalent to $\sqrt{16} = 4$ $sqrt16 = 4$ )

Therefore,

${log}_{16} (4) = \frac{1}{2}$ $log_16(4) = color(blue)(1/2$

How do you evaluate f(x)=log16xf(x)=log_16x for x=4?