# solve the exponential equation

• Dec 7th 2009, 03:26 PM
cmmason
solve the exponential equation
Solve for x.

pi^7x-1 = e^8x

I think I need to take the natural log of both sides. but I don't know what to do after this step-

The answer should be exact, which means it should be written with ln and pi and all that
• Dec 7th 2009, 04:19 PM
skeeter
Quote:

Originally Posted by cmmason
Solve for x.

pi^(7x-1) = e^(8x)

I think I need to take the natural log of both sides. but I don't know what to do after this step-

The answer should be exact, which means it should be written with ln and pi and all that

next time use parentheses around the entire exponent to make your post clear.

$\displaystyle \pi^{7x-1} = e^{8x}$

$\displaystyle \ln(\pi^{7x-1}) = \ln(e^{8x})$

$\displaystyle (7x-1)\ln{\pi} = 8x$

$\displaystyle 7x \cdot \ln{\pi} - \ln{\pi} = 8x$

$\displaystyle 7x \cdot \ln{\pi} - 8x = \ln{\pi}$

$\displaystyle x(7\ln{\pi} - 8) = \ln{\pi}$

$\displaystyle x = \frac{\ln{\pi}}{7\ln{\pi} - 8}$