Solve the equation by converting to a common base:

Question

Show step by step work:

1⁄125×25^17x-31=125^52x-42

Answer 1

Hello, Mona,

I'm not completely positive, but please check my logic on how this might be approached.

1⁄125×25^(17x-31)=125^(52x-42)

I will try to make both sides the same base. I can anticipate that 5 might work, so let's try.

1/125 is the same as 5^-3.

25^(17x-31) can also be expressed as 5^2(17x-31) or 5^(34x-62)

Combining the two we get

(5^-3.)*(5^(34x-62)) = 5^(34x-65)

Let's do the same for the right side:

125^(52x-42)

(5³)^(52x-42)

5^(52x=39)

Now we have both sides expressed as base 5:

5^(34x-65) = 5^(52x=39)

Since the bases are the same, we know their exponents must be equal:

34x-65 = 52x-39

Solving:

18x = -26

x = (26/16)

x = 1(5/8)

This isn't a very satisfying answer, for so much work. So please check my calculations. The approach should be valid. But I'm out of time to double check the steps.

I hope this helps,

Bob

Bob