125(^3x-1)=25(^2-x)...x=?

Question

Solve the equation 125(^3x-1)=25(^2-x), Giving your answer as a fraction

Can somebody please help?

Answer 1

125^(3x-1) = 25^(2-x) (Assuming THIS is what you actually mean)

Well 125 = 5³ and 25 = 5²

So 125^(3x-1) = 5³^(3x-1) = 5^(9x - 3)
and 25^(2-x) = 5²^(2-x) = 5^(4 - 2x)

Equating coefficients as the bases are the same (both 5)

Therefore 9x - 3 = 4 - 2x
So 11x = 7
x = 7/11

Check:

LHS = 125^(3x-1)
= 125^(21/11 - 1)
= 125^(10/11)
= 5^(30/11)

RHS = 25^(2-x)
= 25^(2 - 7/11)
= 25^(15/11)
= 5^(30/11)
= LHS YESSSSSSSSSSSSSSSSSSSSS!!!!!!

Answer 2

well 125 can be written as 5^3, and 25 as 5^2.

so....

(5^3)^(3x - 1) = (5^2)^(2-x)

Then, since raising an exponent to an exponent is the same as multiplying:

5^(3(3x - 1)) = 5^(2(2 - x))

So

3(3x - 1) = 2(2 - x)
9x - 3 = 4 - 2x
11x = 7
x = 7/11

Answer 3

125(^3x-1)=25(^2-x)
5³(³x-1) = 5²(²-x)
Working exponents:
3(3x-1) = 2(2-x)
9x - 3 = 4 - 2x
9x + 2x = 4 + 3
11x = 7
x = 7/11
The answer is 7/11.
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Answer 4

I am just putting the terms in meaningful form

125^(3x-1)=25^(2-x)
[(5)^3]^(3x-1) = [(5)^2(2-x)]

Equating the powers of 5
3(3x-1) = 2(2-x)

x=7/11

Answer 5

My advice is to notice that 5^2=25 and 5^3=125.

These exercises are designed to test your use of the properties of exponents.

Divide both sides by 25 and note that

If a^b = a^c then b=c

Answer 6

125(^3x-1)=25(^2-x), I assume you meant
125^(3x-1)=25^(2-x)
5^3(3x-1)=5^2(2-x)
3(3x-1)=2(2-x)
9x-3=4-2x
11x=7
x=7/11

Answer 7

125^(3x - 1) = 25^(2 - x)
(5^3)^(3x - 1) = (5^2)^(2 - x)
5^(3(3x - 1)) = 5^(2(2 - x))
5^(9x - 3) = 5^(4 - 2x)
9x - 3 = 4 - 2x
11x = 7
x = (7/11)

Answer 8

I'll give you three hints:

1. Write both the sides of the equation in such away that the base of the exponent is 5.

2. 125 = 5^3 and 25 = 5^2

3. when you complete that both sides will be of the form 5^(some expression). Those expressions will have to be equal.

Answer 9

125(^3x-1)=25(^2-x)
Here's an alternate method:
log 125^(3x-1) = log25^(2-x)
(3x-1)log 5^3 = (2-x) log5^2
3(3x-1)log5 = 2(2-x) log5
9x-3 = 4-2x [after dividing both sides by log 5]
11x=7
x=7/11

Isn't it great how consistent math is?

Answer 10

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