SOLUTION: Solve: a) log(x-2)+log(x+1)=1 b) 4(^1-x)=3*5^x c) logbase2(1-x)+logbase2(4x+1)=0

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Question 129852: Solve:
a) log(x-2)+log(x+1)=1
b) 4(^1-x)=3*5^x
c) logbase2(1-x)+logbase2(4x+1)=0
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
a)
log(x-2)+log(x+1)=1
log((x-2)(x+1))=1
log(x^2-x-2)=1
10^log(x^2-x-2)=10^1
x^2-x-2=10
x^2-x-12=0
(x-4)(x+3)=0
x=4, x=-3 (extraneous)
x=4
.
c)
logbase2(1-x)+logbase2(4x+1)=0
log[2]((-x+1)(4x+1))=0
log[2](-4x^2+3x+1)=0
2^log[2](-4x^2+3x+1)=2^0
-4x^2+3x+1=1
-4x^2+3x=0
x(-4x+3)=0
x=0, x=3/4
.
Ed