Question #3f497

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Answer 1 · 2014-10-19T13:28:37

Let us solve the equation step by step.

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

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

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

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

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

by dividing by $10$ $10$ ,

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

by matching the powers,

$5 x = 4$ $5x=4$

by dividing by $5$ $5$ ,

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

I hope that this was helpful.