Question #3f497

1 Answer
Oct 19, 2014

Let us solve the equation step by step.

3^{5x}+3^{5x+2}=810

by the exponential property: b^{x+y}=b^x cdot b^y,

Rightarrow 3^{5x}+3^{5x}cdot3^2=810

by factoring out 3^{5x},

Rightarrow 3^{5x}(1+3^2)=810 Rightarrow 3^{5x}cdot 10=810

by dividing by 10,

3^{5x}=81=3^4

by matching the powers,

5x=4

by dividing by 5,

x=4/5


I hope that this was helpful.