question...

[Tascja]

how would i go about doing this question?

5^2x - 30(5^x) + 125 = 0

 

[TchrQbic]

how would i go about doing this question?

5^2x - 30(5^x) + 125 = 0

First, you need to rewrite the terms so that you have a more usable form. You have one term involving 5^x, so write the first term similarly.

5^(2x) = (5^x)²

Using that format, your problem becomes

(5^x)² - 30(5^x) + 125 = 0

Now, let a = (5^x) and rewrite the equation in terms of a.

a² - 30a + 125 = 0

Solve that as usual, then once you have solutions, replace a with 5^x and finish getting the final values of x.

 

[pka]

Can you solve this: \(\displaystyle w^2 - 30w + 125 = 0\).
\(\displaystyle (w - 5)(w - 25) = 0\)?

If we let \(\displaystyle w = 5^x\) then the solutions are \(\displaystyle 5^x = 5\quad \& \quad 5^x = 25 = 5^2\).