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rite2deepti
If 25(5^x) = 1 then x=

A. –2
B. –1
C. 0
D. 1
E. 2

I have probelm with this question .
I solved it like 5^2(5^x)=1
2+x=1
X=-1

But my answer is wrong or the answer from the source is wrong please help ....


Hey Deepti,

You have solved the question correctly till this point:

\(5^{(2+x)} = 1\)

But please remember that while equating the powers from LHS and RHS, the base should be the same. In the LHS, the base is 5 and on the right hand side(RHS), the base is 1, so we need to convert 1 to the base 5, which can be easily done, by write 1 as \(5^0\)

Now you will have \(5^{(2+x)} = 5^0\)

After this, you can equate the powers, which will give you \(2 + x = 0\) and \(x = -2\)

I hope this clears your doubt.


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Saquib
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rite2deepti
If 25(5^x) = 1 then x=

A. –2
B. –1
C. 0
D. 1
E. 2

(5^2)(5^x) = 5^0

5^(2 + x) = 5^0

2 + x = 0

x = -2

Alternate Solution:

25(5^x) = 1

5^x = 1/25

5^x = 5^-2

x = -2

Answer: A
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