How do you solve 25^x=1/125 ?

2 Answers

x= -3/2

x=-1.5

Explanation:

1/125 = 5^-3

so 25^x = 5^-3

and (5^2)^x = 5^-3

so 5^(2x) = 5^-3

and now that the bases are the same you can remove them:

2x = -3

x= -3/2

x=-1.5

Mar 7, 2018

Here we might need a common base, or you can use log and a calculator
x= -3/2 or -1.5

Explanation:

Method 1- Common base
I noticed that both 25 and 125 are 5 to some power.
So therefore I can safely state that:
5^(2x)= 1/5^3
5^(2x)= 5^(-3)
Now that we have a common base of 5, I can just set the exponents equal to one another.
2x=-3
x=-3/2

Method 2- Use log
25^x=1/125 is the same thing as log_25(1/125)=x
"plug" log_25(1/125) "into your calculator and you should still get" -1.5