Hi there,

Can someone please show me how to solve the following equation:

5^x + 25^(2x) = 150

Any help will be greatly appreciated,

Cheers

2. Originally Posted by tazrulz99
Hi there,

Can someone please show me how to solve the following equation:

5^x + 25^(2x) = 150

Any help will be greatly appreciated,

Cheers
Hmm, just check that you didn't make a typo somewhere, it does look a bit like a hard equation for pre-algebra i would say.

$\displaystyle 5^x + 25^{2x} = 150$

$\displaystyle 5^x + 5^{4x} = 150$

$\displaystyle Set \ 5^x = k$

$\displaystyle k + k^4 = 150$

$\displaystyle k^4 + k - 150 = 0$

I quickly solved it by drawing a graph (See the attached image)

And it seems the answers are -3,54 and 3.46

3. ## .

Ok and from there you solve with logs. Thanks!

4. Originally Posted by tazrulz99
Ok and from there you solve with logs. Thanks!
Yes because $\displaystyle k = 5^x$

But $\displaystyle 5^x$ cannot be equal to $\displaystyle -3,54$

Thus $\displaystyle 5^x$= $\displaystyle 3,46$

I found: $\displaystyle x = 0,77$