SOLUTION: Hi:) I need some help:) Solve for x: 1) logbase[5](x+1)+logbase[5](x-2)=logbase[5] 4 2) 1/3 logbase[3] 27+logbase[3] x = 4^(1/2) 3) logbase[2](x-6)+logbase[2](x)=4 4) logbas

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Question 185156: Hi:) I need some help:)
Solve for x:
1) logbase[5](x+1)+logbase[5](x-2)=logbase[5] 4
2) 1/3 logbase[3] 27+logbase[3] x = 4^(1/2)
3) logbase[2](x-6)+logbase[2](x)=4
4) logbase[4](2x+1)-logbase[4](x-2)=1
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
You will need to apply "log rules".
You can review them at:
http://www.purplemath.com/modules/logrules.htm
.
1) logbase[5](x+1)+logbase[5](x-2)=logbase[5] 4
logbase[5](x+1)(x-2)=logbase[5] 4
logbase[5](x^2-x-2)=logbase[5] 4
x^2-x-2= 4
x^2-x-6= 0
(x-3)(x+2) = 0
x = {3,-2}
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2) 1/3 logbase[3] 27+logbase[3] x = 4^(1/2)
logbase[3] 27^(1/3) +logbase[3] x = 4^(1/2)
logbase[3] 3 +logbase[3] x = 2
logbase[3] 3x = 2
3x = 3^2
3x = 9
x = 3
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3) logbase[2](x-6)+logbase[2](x)=4
logbase[2](x-6)(x)=4
(x-6)(x)=2^4
x^2-6x=16
x^2-6x-16 = 0
(x-8)(x+2) = 0
x = {8,-2}
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4) logbase[4](2x+1)-logbase[4](x-2)=1
logbase[4](2x+1)(x-2)=1
(2x+1)(x-2)=4^1
2x^2-4x+x-2=4
2x^2-3x-2=4
2x^2-3x-6=0
(2x+2)(x-3) = 0
x={-1, 3}