SOLUTION: I have been having a really hard problem with these logs 1. Log base 8 X=1/3 2. Log e^x^2=125 3. Solve for X: Log(5-2x)=log (3x+1) 4. Solve for X: Log(x+1)-Log(x-1)=1

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I have been having a really hard problem with these logs 1. Log base 8 X=1/3 2. Log e^x^2=125 3. Solve for X: Log(5-2x)=log (3x+1) 4. Solve for X: Log(x+1)-Log(x-1)=1      Log On


   

Question 204536: I have been having a really hard problem with these logs
1. Log base 8 X=1/3
2. Log e^x^2=125
3. Solve for X: Log(5-2x)=log (3x+1)
4. Solve for X: Log(x+1)-Log(x-1)=1
Found 2 solutions by alicealc, nerdybill:
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
Number 1.
X = 8 ^ (1/3) = 2 ^ (3 * 1/3) = 2
Number 2.
e^x^2 = 10^125
x^2 = ln(10^125)
x+=+sqrt%28ln%2810%5E125%29%29
Number 3.
5 - 2x = 3x + 1
5 - 1 = 3x + 2x
4 = 5x
x = 4/5
Number 4.
log%28%28x%2B1%29%2F%28x-1%29%29=1
%28x%2B1%29%2F%28x-1%29=10%5E1
x + 1 = 10*(x- 1)
x + 1 = 10x - 10
1 + 10 = 10x - x
11 = 9x
x = 11/9

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
1. Log base 8 X=1/3
x = 8^(1/3)
x = 2
.
2. Log e^x^2=125
x^2 = ln(125)
x^2 = 4.8283
x = 2.197
.
3. Solve for X: Log(5-2x)=log (3x+1)
5-2x = 3x+1
5 = 5x+1
4 = 5x
4/5 = x
0.8 = x
.
4. Solve for X: Log(x+1)-Log(x-1)=1
Log[(x+1)/(x-1)]=1
(x+1)/(x-1)= 10^1
(x+1)/(x-1)= 10
(x+1) = 10(x-1)
x+1 = 10x-10
1 = 9x-10
11 = 9x
11/9 = x
1.222 = x