Question

1) log1/9(x+2)+3log27(x+2)=1
2) log16x+log8x+log2x= 19/12

Answer 1

1) $log_{ frac{1}{9}}(x+2)+3log_{27}(x+2)=1$
$log_{3^{-1}}(x+2)+3log_{3^{3}}(x+2)=1$
$-0.5*log_{3}(x+2)+log_{3}(x+2)=1$
$0.5*log_{3}(x+2)=1$
$log_{3}(x+2)=2$
$x+2=9, x=7$

2) $log_{16}x+log_{8}x+log_{2}x= frac{19}{12}$
$log_{2^{4}}x+log_{2^{3}}x+log_{2}x= frac{19}{12}$
$frac{1}{4}*log_{2}x+ frac{1}{3}*log_{2}x+log_{2}x= frac{19}{12}$
$3log_{2}x+ 4log_{2}x+12log_{2}x=19$
$19log_{2}x=19$
$log_{2}x=1$
$x=2$