precalc question

Question

25^4-x = 125^3x+1

Answer 1

25^(4-x) = 125^(3x+1) solve for x

rewrite with both sides as base 25, then set powers equal

Answer 2

Hi Maya C

Since, you did not use parentheses, if you meant to write the following:

25^{(4 - x)} = 125^{(3x +1)}

You need to find a common base, since

25 = 5²

125 = 5³

So you have

5^2(4-x) = 5^{3(3x +1)}

Then you can solve for x and check

2(4 -x) = 3(3x + 1)

8 - 2x = 9x + 3

8 - 3 = 9x +2x

5 = 11x

5/11 = x

Checking

25^39/11 = 125^26/11 = 90434.21186

Hope this helps

Answer 3

25^4-x = 125^3x+1

(5²)^4-x = (5³)^3x+1

5^2*(4-x) = 5^3*(3x+1)

If the bases are the same, the exponents must be equal.

2*(4-x) = 3*(3x+1)

8 - 2x = 9x + 3

Subtract 3 from both sides and add 2x to both sides of the above equation:

5 = 11x

x = 5/11

Substituting this value back into the original equation verifies that this is the correct answer.