Question #3f497

1 Answer
Oct 19, 2014

Let us solve the equation step by step.

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

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

$R i g h t a r r o w {3}^{5 x} + {3}^{5 x} \cdot {3}^{2} = 810$

by factoring out ${3}^{5 x}$,

$R i g h t a r r o w {3}^{5 x} \left(1 + {3}^{2}\right) = 810 R i g h t a r r o w {3}^{5 x} \cdot 10 = 810$

by dividing by $10$,

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

by matching the powers,

$5 x = 4$

by dividing by $5$,

$x = \frac{4}{5}$

I hope that this was helpful.