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What is the solution to this equation? 125^x-2=(1/25)^3x A. -9/2 B. -2/3 C. 2/3 D. 2/9

User Tanjir
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Answer:

C.

Explanation:

1. Simplify the bases: Rewrite 125 as 5^3 and (1/25) as (1/5)^2.

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

2. Apply the power of a power rule: Multiply the exponents when raising a power to another power.

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

3. Simplify the exponents: Distribute the exponents.

5^(3x-6) = (1/5)^(6x)

4. Convert the bases to a common base: Both sides of the equation have bases of 5, so we can rewrite (1/5) as 5^(-1).

5^(3x-6) = 5^(-6x)

5. Set the exponents equal to each other: Since the bases are the same, the exponents must be equal.

3x - 6 = -6x

6. Solve for x: Combine like terms and isolate x.

3x + 6x = 6

9x = 6

x = 6/9

x = 2/3

Therefore, the value of x that satisfies the equation is 2/3.

User Bill Barksdale
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