# Thread: Help! Equations with exponets :(

1. ## Help! Equations with exponets :(

I would greatly appreciate if someone could help me on this one, thank you so much:

Solve for x to eight decimal places if

2^(2x – 1) = 3^(x-2)

back into original and show that it
will make each side equal.

2. Originally Posted by Alesa'7
I would greatly appreciate if someone could help me on this one, thank you so much:

Solve for x to eight decimal places if

2^(2x – 1) = 3^(x-2)

back into original and show that it
will make each side equal.
Hello!

Note that $\displaystyle 2^{2x-1}=3^{x-1}\implies 4^x 2^{-1}=3^x 3^{-1}\implies\left(\tfrac{4}{3}\right)^x=\tfrac{2}{3} \implies x=\frac{\ln\left(\tfrac{2}{3}\right)}{\ln\left(\tf rac{4}{3}\right)}$

Now you can plug this into your calculator and get an approximation to 8 decimal places.

--Chris

3. is it -1.40942084 ?

4. lol sry for being nosy.. juss looking around at the different post,while I wait till someone helps with mine... This place is so cool