SOLUTION: Solve for x: logbase5(x+1)+logbase5(x-3)=1

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve for x: logbase5(x+1)+logbase5(x-3)=1      Log On


   

Question 128052: Solve for x:
logbase5(x+1)+logbase5(x-3)=1
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%2C%28x%2B1%29%29%2Blog%285%2C%28x-3%29%29=1

First thing is to use the rule that log%28b%2Ca%29%2Blog%28b%2Cc%29=log%28b%2Cac%29, so

log%285%2C%28x%2B1%29%28x-3%29%29=1

Next, we note that if log%28b%2Ca%29=y then b%5Ey=x, so

5%5E1=%28x%2B1%29%28x-3%29

5=x%5E2-2x-3

x%5E2-2x-8=0

%28x-4%29%28x%2B2%29=0

x=4 or x=-2

However, x=-2 means that x-3%3C0 and log%28b%2Cx%29 is not defined for x%3C0, therefore we need to exclude the second root.

The solution set consists of the single element 4.