SOLUTION: log base 7 (x+4) - log base 7 (x) = 2 How would I solve this? {{{log(7,(x+4))-log(7,x)=2}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: log base 7 (x+4) - log base 7 (x) = 2 How would I solve this? {{{log(7,(x+4))-log(7,x)=2}}}      Log On


   

Question 719786: log base 7 (x+4) - log base 7 (x) = 2
How would I solve this?
log%287%2C%28x%2B4%29%29-log%287%2Cx%29=2
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Your key to begin is log%28b%2CX%29%2Blog%28b%2CY%29=log%28b%2CXY%29, and log%28b%2CX%29-log%28b%2CY%29=log%28b%2CX%2FY%29.

log%287%2C%28x%2B4%29%29-log%287%2Cx%29=2
log%287%2C%28%28x%2B4%29%2F%28x%29%29%29=2
Translate into exponential form:
highlight%287%5E2=%28x%2B4%29%2Fx%29
49x=x%2B4
48x=4
highlight%28x=12%29