How do you evaluate log_15(15)?

1 Answer
Lotusbluete
Dec 3, 2015

log_a(a) = 1 holds for any positive integer a.

Explanation:

You are basically searching for x so that

log_(15)(15) = x

The inverse function of the log_15(z) is 15^zwhich means that
log_15(15^z) = z and also 15^(log_15(z)) = z always hold.

This means that to "get rid" of the logarithmic term, you can perform 15^z on both sides of your equation:

color(white)(xxx)15^(log_15(15)) = 15^x

<=> color(white)(xxxxx) 15 = 15^x

<=> color(white)(xxxxx) 15^1 = 15^x

So you can see that x = 1 which means that

log_15(15) = 1

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