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)}`