Solving a log equation with two variables

D. Martin · #1 $Old$ November 30th, 2008, 09:56 PM

Blue represents the base of the log.
Problem: $log [color=royalblue](2a)[/color] (4a^2)^3 = x$

Attempted Solution: I converted the logarithm into exponential form.

$2a^x = (4a^2)^3$
$2a^x = 64a^6$
$2a^x/2 = 64a^6/2$
$a^x = 32a^6$

I cannot see where to go from here.

Could someone please help?

Chris L T521 · #2 $Old$ November 30th, 2008, 10:06 PM

Quote:

Originally Posted by D. Martin $View Post$

Blue represents the base of the log.
Problem: $log [color=royalblue](2a)[/color] (4a^2)^3 = x$

Attempted Solution: I converted the logarithm into exponential form.

$2a^x = (4a^2)^3$
$2a^x = 64a^6$
$2a^x/2 = 64a^6/2$
$a^x = 32a^6$

I cannot see where to go from here.

Could someone please help?

Note that $\log_{2a}\left[(4a^2)^3\right]=3\log_{2a}(4a^2)=3\log_{2a}\left[(2a)^2\right]=6\log_{2a}(2a)=6$

Thus, $\color{red}\boxed{x=6}$

Does this make sense?