How to solve this? *log*

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

1 Answer
Apr 18, 2016

#x=-2#

Explanation:

Use the rule #(a^b)^c=a^(bc)# to simplify the left hand side of the equation. Also, write #sqrt(5^x)# as #(5^x)^(1/2)# and simplify it using the same rule, to give:

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

Now, note that #0.2=1/5=5^-1#.

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

Simplify the right hand side using the rule #a^b(a^b)=a^(b+c)#.

#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#