5^log5 (x) + log5 (2) =5 solve for x

Question

Don't know exactly how to do this problem.

Answer 1

The first term is just x; the second term is log₅2 which is a decimal that we can compute

using change-of-base = (ln2)/(ln 5)= 0.430677, approx.

 

So the equation becomes    x + 0.430677 = 5  and you take it from here!

 

Answer 2

Something about exponents and logs...  they "undo" each other.

 

So 5^log₅x = x

 

Now your equation is x + log₅2 = 5

 

so subract the log₅2 from both sides, and will have

 

x = 5 - log₂5