Question

Помогите 5^(x+4)+3*4^(x+3)=4^(x+4)+4*5^(x+3)

Answer 1

$5^{x+4}+3*4^{x+3}= 4^{x+4}+4*5^{x+3}$
$5^{x}*5^{4}+3*4^{x}*4^{3}= 4^{x}*4^{4}+4*5^{x}*5^{3}$
$5^{x}*625+3*4^{x}*64= 4^{x}*256+4*5^{x}*125$
$5^{x}*625+4^{x}*192= 4^{x}*256+5^{x}*500$
$5^{x}*625- 5^{x}*500= 4^{x}*256 - 4^{x}*192$
$125*5^{x} = 64*4^{x}$ //$4^{x}$
$125* (\frac{5}{4})^{x} = 64$ //125
$(\frac{5}{4})^{x} = \frac{64}{125}$
$(\frac{5}{4})^{x} = (\frac{5}{4})^{-3}$
значит x=-3