Question #3f497

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Answer 1 · 2014-10-19T13:28:37

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.