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

Printable View

- Dec 7th 2009, 03:26 PMcmmasonsolve 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 PMskeeter
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})

$

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

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

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

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

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