How do you solve $4log_4 (x) - 9log_x (4) = 0$ ?

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Answer 1 · 2016-03-14T15:08:13

You must first simplify using the rule $log_am = logm/loga$

First, we must use the rule $alogn = logn^a$

$log_4(x^4) - log_x(262144) = 0$

$(logx^4)/(log4) - (log262144)/logx = 0$

Place on a common denominator.

$(logx(logx^4))/(log4(logx)) - (log4(log262144))/(logx(log4)) = 0$

Convert to exponential form.

$x^5/1048576 = 10^0$

$x^5 = 1048576$

$x = root(5)1048576$

$x = 16$

Hopefully this helps!

How do you solve 4log_4 (x) - 9log_x (4) = 04log_4 (x) - 9log_x (4) = 0?