SOLUTION: SOLVE for x: a) logbase3 x + logbase3 (x-8)=2 b) logbase4 (x+2)+logbase4(x-4)=2 c) logbase2 (5x-2)-logbase2 2 =1/2 logbase2 36 + 2 logbase2 3

Question 185084: SOLVE for x:
a) logbase3 x + logbase3 (x-8)=2
b) logbase4 (x+2)+logbase4(x-4)=2
c) logbase2 (5x-2)-logbase2 2 =1/2 logbase2 36 + 2 logbase2 3
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a)
logbase3 x + logbase3 (x-8)=2
3^log[3]x * 3^log[3](x-8)=3^2
x(x-8)=9
x^2-8x-9=0
(x-9)(x+1)=0
x=9, x<>-1 because there is no log of a negative number.
.
b)
logbase4 (x+2)+logbase4(x-4)=2
4^log[4](x+2) * 4^log[4](x-4)=4^2
(x+2)(x-4)=16
x^2-2x-8=16
x^2-2x-24=0
(x-6)(x+4)=0
x=6
.
c)
logbase2 (5x-2)-logbase2 2 =1/2 logbase2 36 + 2 logbase2 3
2^log[2](5x-2) / 2^log[2]2=2^log[2]6 * 2^log[2]9 explanation:{1/2 log 36= sqrt(36)}
(5x-2)/2=6*9
5x-2=108
5x=110
x=22
.
Ed

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