Question

Write expression as a single logarithm 5 log3^x+7 log3^y

Answer 1

$Use:\\logx^n=n\cdot logx\\\\logc+logy=log(xy)\\\\\left(a^n\right)^m=a^{n\cdot m}\\\\a^n\cdot a^m=a^{n+m}\\========================\\\\5log3^x+7log3^y=log\left(3^x\right)^5+log\left(3^y\right)^7=log3^{5x}+log3^{7y}\\\\=log\left(3^{5x}\cdot3^{7y}\right)=log\left(3^{5x+7y}\right)\\\\\boxed{5log3^x+7log3^y=log\left(3^{5x+7y}\right)}$