how to solve?

Question

The symbol log x indicates that it is a base 10 logarithm. The solution of the equation log (x-1)=2 - log (25) is an integer. What is your answer? (Give number as an interger only)

Answer 1

log (x-1) = 2 - log (25)

 

We need to solve for x.  To do that, raise both sides as exponents of 10:

 

10^log(x-1) = 10^(2-log(25))

 

Now 10^log(a) = a and 10^(a-b) = 10^a/10^b .  Hence:

 

x-1 = 10²/10^log(25)

 

x-1 = 100/25

 

Solve for x.