5^(2x) + 5^(3x-1) = 150

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- Jul 16th 2010, 09:54 PMZharif93logarithm
5^(2x) + 5^(3x-1) = 150

- Jul 16th 2010, 10:00 PMProve It
Are you sure this isn't supposed to be

$\displaystyle 5^{2x} \cdot 5^{3x-1} = 150$? - Jul 16th 2010, 10:03 PMZharif93
im not sure , my friend ask me this question

- Jul 17th 2010, 04:23 AMHallsofIvy
$\displaystyle 5^{2z}= (5^x)^2$ and $\displaystyle 5^{3x-1}= \frac{(5^x)^3}{5}$

Your equation is $\displaystyle (5^x)^2+ \frac{(5^x)^3}{5}= 150$. If you let $\displaystyle y= 5^x$ you have $\displaystyle y^2+ y^3/5= 150$ or the cubic polynomial $\displaystyle y^3+ 5y^2= 750$. Any**rational**solution for y must be a factor of 750. I suggest you whack your friend about the ears!