Question

$ f( x) =2^{x+3}$, $ \frac{f( 2x-5)}{f( x-1) } =256 $ ise $x=?$

Answer 1

$f(2x-5)=2^{(2x-5)+3}=2^{2x-2}$

$f(x-1)=2^{(x-1)+3}=2^{x+2}$

$\frac {f(2x-5)}{f(x-1)}=\frac {2^{2x-2}}{2^{x+2}}=2^{(2x-2)-(x+2)}=2^{x-4}$

$256=2^{8}$ olduğuna göre

$x-4=8$

$x=12$