SOLUTION: log base 3 (x+1) - log base 3 x = log base 3 8

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: log base 3 (x+1) - log base 3 x = log base 3 8      Log On


   

Question 186942: log base 3 (x+1) - log base 3 x = log base 3 8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C%28x%2B1%29%29-log%283%2C%28x%29%29=log%283%2C%288%29%29 Start with the given equation.


log%283%2C%28%28x%2B1%29%2Fx%29%29=log%283%2C%288%29%29 Combine the logs on the left side using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


3%5Elog%283%2C%28%28x%2B1%29%2Fx%29%29=3%5Elog%283%2C%288%29%29 Raise both sides as exponents with the base of 3 (this will cancel out the log base 3)


%28x%2B1%29%2Fx=8 Simplify


x%2B1=8x Multiply both sides by 8.


x=8x-1 Subtract 1 from both sides.


x-8x=-1 Subtract 8x from both sides.


-7x=-1 Combine like terms on the left side.


x=%28-1%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=1%2F7 Reduce.


----------------------------------------------------------------------

Answer:

So the answer is x=1%2F7 which approximates to x=0.143.