# Hello friends, please, I need to know how to get the answer out of this exponential equation? thank you

##### 1 Answer

#### Explanation:

First, we will use the properties of exponents that

#a^(x+y) = a^xa^y# #(a^x)^y = a^(xy) = (a^y)^x#

With these manipulations, we can see this has the form of a quadratic equation, but with

#=(2+-sqrt(16))/(2/9)#

#=(2+-4)/(2/9)#

#=9+-18#

Note that

The answer is pretty clear at this point, but we can justify it properly by using logarithms. We will use the following properties of logarithms:

#log(a^x) = xlog(a)# #log_a(a) = 1#

With those, we have

Finally, we can check our answer:

as desired.