Question

если
$2 {}^{x} = 7 {}^{y} = 6 {}^{z}$
то
$4 {}^{ \frac{x}{y} } + 8 {}^{ \frac{x}{z} } =$
?​

Answer 1

$2^x=7^y=>x=log_27^y=>x=y\cdot log_27=>\dfrac{x}{y}=log_27=log_449\\ 2^x=6^z=>x=log_26^z=>x=z\cdot log_26=>\dfrac{x}{z}=log_26=log_8216\\ 4 {}^{ \frac{x}{y} }  + 8 {}^{ \frac{x}{z} }  = 4^{log_449}+8^{log_8216}=49+216=265$