If $17^m=6$ , what is m?

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Answer 1 · 2017-06-26T16:53:57

$m = ln(6)/ln(17)$

Given $17^m=6$

Use the natural logarithm on both sides:

$ln(17^m) = ln(6)$

NOTE: You can use any base logarithm you like; I have arbitrarily chosen natural logarithms.

Use the property of logarithms $ln(a^c) = cln(a)$ :

$mln(17) = ln(6)$

Divide both sides by $ln(17)$

$m = ln(6)/ln(17)$

If 17^m=617^m=6, what is m?