\(a^log_ab=b\)
a^log_ab=b
Saw it in a textbook (Revision) How does it work ?
+128474 a^ ( loga b) = b (1)
I'll admit that when I first saw this in Algebra it was a little tough to see
Let's prove this is true :
Take the log of both sides
log a ^ (loga b) = log b and by a log property we have
( loga b) * log a = log b divide both sides by log a
loga b = log b /log a by the change-of-base rule for logs we can write
log b / log a = log b / log a
Since this is an identity....then so is (1)
