SOLUTION: Solve the equation: 1n x = 1n 2 + 1n (3x - 1) I know the answer is 2/5 from the answers in the back of the book. I need to know how the solution was solved. I really appreci

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Question 80458This question is from textbook
: Solve the equation: 1n x = 1n 2 + 1n (3x - 1)
I know the answer is 2/5 from the answers in the back of the book.
I need to know how the solution was solved.
I really appreciate your help.
This question is from textbook

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Given:
.
1n = 1n + 1n
.
Collect the logarithms that contain x on one side of the equation. You can do that by
subtracting ln from both sides of the equation. When you do that subtraction
you get:
.
ln - ln = ln
.
Now apply the rule that the difference in two logarithms is the same as the log of their division.
In equation form that rule says:
.
ln - ln = ln
.
With that rule the equation becomes:
.
ln = ln
.
Look at this carefully ... comparing the left side to the right side. For this to be
true the two logarithms must be equal, and this means that:
.

.
To get rid of the denominator, multiply both sides by the denominator of to
get:
.

.
On the left side the multiplier cancels with the denominator. And multiplying the right
side, gives:
.

.
and it reduces to:
.

.
Solve this as you would any equation. You need to gather all the terms that contain x
on one side of the equation and everything else on the other side. You can do this by
subtracting 6x from both sides to get:
.

.
combine the terms on the left side and the result is:
.

.
solve for x by dividing both sides by -5 and the outcome is:
.

.
and that's how to get the book answer. Hope this helps to familiarize you with logarithms.