# How to solve this? *log*

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#(5^(x+1))^2 = 0.2sqrt(5^x)#

##### 1 Answer

Apr 18, 2016

#### Explanation:

Use the rule

#5^(2x+2)=0.2(5^(1/2x))#

Now, note that

#5^(2x+2)=5^-1(5^(1/2x))#

Simplify the right hand side using the rule

#5^(2x+2)=5^(1/2x-1)#

Now, since we have two exponential functions with the same base being equal, we also know that their exponents will be equal.

#2x+2=1/2x-1#

#3/2x=-3#

#x=-3(2/3)=-2#