SOLUTION: How do I simplify this and find x? log4(x-4) + log4(x+2) = log7(49)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do I simplify this and find x? log4(x-4) + log4(x+2) = log7(49)      Log On


   

Question 377497: How do I simplify this and find x?
log4(x-4) + log4(x+2) = log7(49)
Answer by vasumathi(46) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%28x-4%29%29+ log%284%2C%28x%2B2%29%29= log%287%2C%2849%29%29
since the bases on the left side are same that is 4 we can combine them using the laws of logarithms
log%284%2C%28%28x-4%29%28x%2B2%29%29%29= log%287%2C%287%5E2%29%29
log%284%2C%28%28x-4%29%28x%2B2%29%29%29=2 log%287%2C%287%29%29
log%284%2C%28%28x-4%29%28x%2B2%29%29%29= 2*1 (since log%287%2C%287%29%29=1 as the logarithm of a number to the same base is 1)
log%284%2C%28%28x-4%29%28x%2B2%29%29%29=2
(x-4)(x+2)= 4^2 = 16
x^2 -2x-8= 16
x^2-2x-8-16=0
x^2-2x-24=0
(x-6)(x+4)=0
so we have x = 6 and x = -4