SOLUTION: Can you help me workout these logarithms questions: 1) 2log(5x)=10 2) log(x-2)-log(x-3)=3 3) 46+3Inx=10 4) In(x+1)=3

Question 227695: Can you help me workout these logarithms questions:
1) 2log(5x)=10
2) log(x-2)-log(x-3)=3
3) 46+3Inx=10
4) In(x+1)=3
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Applying "log rules":
1) 2log(5x)=10
log(5x) = 5
5x = 10^5
x = 10^5/5
x = 20000
.
2) log(x-2)-log(x-3)=3
log[(x-2)/(x-3)] = 3
(x-2)/(x-3) = 10^3
(x-2)/(x-3) = 1000
x-2 = 1000(x-3)
x-2 = 1000x-3000
2998 = 999x
3.001 = x
.
3) 46+3Inx=10
3lnx = -36
ln x = -12
x = e^(-12)
x = 1/e^(12)
x = 6.144*10^(-6)
.
4) In(x+1)=3
x+1 = e^3
x = e^3-1
x = 19.0855
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