SOLUTION: If log(3x-1)-log2=3, what is the value of x THANK YOU

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Question 1009828: If log(3x-1)-log2=3, what is the value of x
THANK YOU
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
start with:

log(3x-1) - log(2) = 3

since log(a) - log(b) = log(a/b), the equation becomes:

log((3x-1)/2) = 3

this is true if and only if 10^3 = (3x-1)/2

since 10^3 = 1000, then:

1000 = (3x-1)/2

multiply both sides of this equation by 2 to get:

3x-1 = 2000

add 1 to both sides of the equation to get:

3x = 2001

divide both sides of the equation by 3 to get:

x = 667

that's your solution.

when x = 667, log(3x-1) - log(2) = 3 becomes log(3*667-1) - log(2) = 3 which becomes 3 = 3.

this confirms the solution is correct.

your solution is that x = 667.


Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

If log(3x-1)-log2=3, what is the value of x
THANK YOU
log (3x - 1) - log (2) = 3

log+%28%283x+-+1%29%2F2%29+=+3 

%283x+-+1%29%2F2+=+10%5E3 -------- Converting to EXPONENTIAL form

%283x+-+1%29%2F2+=+1000 

3x - 1 = 2,000 ------- Cross-multiplying

3x = 2,000 + 1

3x = 2,001

x+=+2001%2F3, or highlight_green%28x+=+667%29