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

Question

not sure how to solve this help please

Answer 1

Using the quotient rule,

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

Then change to exponential form:

10^1 = (2x-1)/(x-3)

then solve:

10(x-3)=2x-1
10x-30=2x-1
8x=29
x=29/8

Answer 2

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Answer 3

x must be > 3
log(2x-1)-log(x-3)=1
<=> log[(2x-1)/(x-3)] = log 10
<=> 2x-1 = 10(x-3)
<=> 8x = 29 <=> x = 29/8 > 3
then the root is x = 29/8

Answer 4

One property of logs says if you take the log of a fraction, you can split it into 2 separate logs with a minus sign separating them.

For example: log(a/b) = log(a) - log(b)

This property works in reverse as well. So for your problem, we combine the 2 log terms on the left hand side into one log expression.

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

Which is equal to 1. log((2x-1)/(x-3)) = 1

Now we need to change this into exponential form to get the x's by itself withought log in our way.

log expressions have base 10, so we can change log((2x-1)/(x-3)) = 1 into 10^1 = (2x-1)/(x-3)

Now we can simplify.

First by cross multiplication we get 10(x-3) = 2x-1

Distribute the 10 to get 10x - 30 = 2x - 1

Subtract 2x from both sides to get 8x - 30 = -1

Now add 30 to both sides to get 8x = 29

Divide both sides by 8 to get x = 29/8

Which is our answer.

P.S. It is a good idea to plug this back into the equation to check.

Answer 5

log(2x - 1) - log(x - 3) = 1
log((2x - 1)/(x - 3)) = 1
(2x - 1)/(x - 3) = 10^1
2x - 1 = 10x - 30
-8x = -29
x = (29/8)

Answer 6

The 29/8 answer is correct. However, when doing these types of equations, ALWAYS check your answer to ensure that your proposed solution doesn't cause a negative logarithm (These don't, but future questions might).

Answer 7

use your scientific calculator. if you don't have one then i am sorry because i don't know how to solve.

Answer 8

29/8....or, 3.625