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How do you evaluate ${log}_{15} (15)$ $log_15(15)$ ?

1 Answer

Dec 3, 2015

${log}_{a} (a) = 1$ $log_a(a) = 1$ holds for any positive integer $a$ $a$ .

Explanation:

You are basically searching for $x$ $x$ so that

${log}_{15} (15) = x$ $log_(15)(15) = x$

The inverse function of the ${log}_{15} (z)$ $log_15(z)$ is $15^{z}$ $15^z$ which means that
${log}_{15} (15^{z}) = z$ $log_15(15^z) = z$ and also $15^{{log}_{15} (z)} = z$ $15^(log_15(z)) = z$ always hold.

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

$\times x 15^{{log}_{15} (15)} = 15^{x}$ $color(white)(xxx)15^(log_15(15)) = 15^x$

$\Leftrightarrow \times \times x 15 = 15^{x}$ $<=> color(white)(xxxxx) 15 = 15^x$

$\Leftrightarrow \times \times x 15^{1} = 15^{x}$ $<=> color(white)(xxxxx) 15^1 = 15^x$

So you can see that $x = 1$ $x = 1$ which means that

${log}_{15} (15) = 1$ $log_15(15) = 1$

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