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

Question 377497: How do I simplify this and find x?
log4(x-4) + log4(x+2) = log7(49)
Answer by vasumathi(46) (Show Source): You can put this solution on YOUR website!
+ =
since the bases on the left side are same that is 4 we can combine them using the laws of logarithms
=
=2
= 2*1 (since =1 as the logarithm of a number to the same base is 1)
=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

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