How do I solve $ln(1/2)^m = ln2$ ?

Question

3642 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-01T07:26:25

Two ways...

One is simply recognizing that by algebra, $2^(-1) = 1/2$ . Hence, $m = -1$ by inspection, i.e. $(2^(-1))^(-1) = 2 = (1/2)^(-1)$ .

Another way is that anytime you see an exponent, try taking the $ln$ of both sides.

$ln(1/2)^(m) = ln2$

Use the property that

$lna^b = blna$

Thus, we get:

$mln(1/2) = ln2$

$mln(2)^(-1) = ln2$

$-mln2 = ln2$

$=> m = -1$

How do I solve ln(1/2)^m = ln2ln(1/2)^m = ln2?