Question

FIND X WHEN LOG 32 BASE 4 = X-4

Answer 1

Step-by-step explanation:

$log_4 32=x-4 \\ \therefore \frac{log \: 32}{log \: 4} = x - 4 \\ \therefore \frac{log \: {2}^{5} }{log \: {2}^{2} } = x - 4 \\ \therefore \frac{5log \: {2}}{2log \: {2}} = x - 4 \\ \therefore \frac{5}{2} = x - 4\\ \therefore 5 = 2(x - 4) \\ \therefore 5 = 2x - 8 \\ \therefore 5 + 8= 2x \\ \therefore 13= 2x \\ \huge \boxed{ \therefore \: x = \frac{13}{2} }$

Answer 2

$\log_432=x-4\\4^{x-4}=32\\2^{2(x-4)}=2^5\\2(x-4)=5\\2x-8=5\\2x=13\\x=\dfrac{13}{2}$