Question
Find $x,$ if $:\log_432 = x - 4$
✓
Answer
Consider the equation
$ \log _4 32=x-4 $
$ \Rightarrow 4^{x-4}=32 $
$ \Rightarrow\left(2^2\right)^{x-4}=2^5 $
$ \Rightarrow 2^{2(x-4)}=2^5 $
$ \Rightarrow 2 x-8=5 $
$ \Rightarrow 2 x=5+8 $
$ \Rightarrow 2 x=13$
$\Rightarrow x=\frac{13}{2}$
$\Rightarrow x=6 \frac{1}{2}$
$ \log _4 32=x-4 $
$ \Rightarrow 4^{x-4}=32 $
$ \Rightarrow\left(2^2\right)^{x-4}=2^5 $
$ \Rightarrow 2^{2(x-4)}=2^5 $
$ \Rightarrow 2 x-8=5 $
$ \Rightarrow 2 x=5+8 $
$ \Rightarrow 2 x=13$
$\Rightarrow x=\frac{13}{2}$
$\Rightarrow x=6 \frac{1}{2}$
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