How do you solve 25x=1125 ?

2 Answers
angus b. · Hriman · EZ as pi
Mar 7, 2018

x=−32

x=−1.5

Explanation:

1125=5−3

so 25x=5−3

and (52)x=5−3

so 52x=5−3

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

2x=−3

x=−32

x=−1.5

Hriman
Mar 7, 2018

Here we might need a common base, or you can use log and a calculator
x=−32or−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:
52x=153
52x=5−3
Now that we have a common base of 5, I can just set the exponents equal to one another.
2x=−3
x=−32

Method 2- Use log
25x=1125 is the same thing as log25(1125)=x
pluglog25(1125)into your calculator and you should still get−1.5

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