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3. Max solved the equation, 5^x+3 = 25^x-2, but made an error. His work is shown

below. Circle his mistake and solve it correctly.

25^x-2=5^x+3

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


5^2x-2=5^x+3

2x-2=x+3

X=5

User Nunzio
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1 Answer

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Max's mistake is in the step where he rewrote 25 as (5^2). This resulted in him raising 5 to the power of 2x-2 instead of (2x-2), which is incorrect.

To solve the equation correctly, we can start with:

5^(x+3) = 25^(x-2)

We can then rewrite 25 as (5^2) and simplify as follows:

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

5^(x+3) = 5^(2x-4)

Now we have the same base on both sides of the equation, so we can equate the exponents:

x + 3 = 2x - 4

Solving for x, we get:

x = 7

Therefore, the solution to the equation is x = 7.

User Gstroup
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