Solving a log equation with two variables

**D. Martin** · November 30th 2008, 07:56 PM

Blue represents the base of the log.
Problem: $log <font color=$ (2a) (4a^2)^3 = x" alt="log (2a) (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** · November 30th 2008, 08:06 PM

Originally Posted by D. Martin

Blue represents the base of the log.
Problem: $log <font color=$ (2a) (4a^2)^3 = x" alt="log (2a) (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?

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