SOLUTION: Please help me and show step by step. Find the largest value of x that satisfies: log_3 (x^ 2) −log_3(x+2)=2 x=___________ ___

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help me and show step by step. Find the largest value of x that satisfies: log_3 (x^ 2) −log_3(x+2)=2 x=___________ ___       Log On


   

Question 998634: Please help me and show step by step.
Find the largest value of x that satisfies:
log_3 (x^ 2) −log_3(x+2)=2
x=_______________
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
log_3 (x^ 2) −log_3(x+2)=2
Raise to the 3 power
x^2/x+2)=9
x^2=9x+18
x^2-9x-18=0
quadratic formula
x=(1/2)+/- (9 +/- sqrt (81+72); sqrt (153)=12.37
largest value is 21.37/2= 10.69
check
log3 (114.28)-log3(12.69)=2
4.31-2.3 (approximate)=2
The largest value is 10.69