# math

write as a single logarithm:

ln(x/x-1)+ ln(x+1/x)- ln(x^2-1)

please show me the steps.

thanx

Michelle, I hope you know the three main rules of logs.
1. log (AB) = log A + log B
2. log (A/B) = log A - log B
3 log A^n - n log A

Using these rules and guessing at your order of operations you would have

ln[{x/(x-1)}{(x+1)/x}all over (x^2-1)]

factoring the bottom into (x+1)(x-1) and reducing the inside of the square bracket I got

ln(1/(x-1)^2)

now using rule #2 and #3 you would get

ln 1 - ln(x-1)^2
= 0-2ln(x-1)
=-2ln(x-1)

thank u sooooo much. been tryin to figure out wat ive been doing wrong.

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### Algebra

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. f ( x ) = 9 x 3 + 2 x 2 − 5 x + 4 and g ( x ) = 5 x 3 − 7 x + 4 . what is f ( x ) − g ( x ) ? Show all of your steps

2. ### Precalculus

Write 4log2+log6-log3 as a single logarithm. Explain with steps please!~~

3. ### Math

Michelle used a \$20 bill to pay for a notebook that only cost p dollars. How much change did Michelle receive from the cashier? Write your answer as an expression.

4. ### Math

Write each logarithmic expression as a single logarithm: Log 2 + 3 log 1

1. ### math (log)

Express as a single logarithm 2log3 + 4log2 I'm confused as to how to do this, I keep getting the wrong answer. Thank you!

2. ### pre calculous

use the properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. show your work ln x^2/y^3 Assuming x,y AND z are positive use properties of logariths to write the

3. ### Algebra

Write the expression as a single logarithm. log_3 40-log_3 10 I'm completely confused with logarithmic equations!! Can someone please please help me understand?

4. ### Math (Condensing logarithmic expression)

Write the expression as the logarithm of a single quantity 3[(ln x) -2ln(x^2+1)]+2 ln 5?

1. ### Math 120

Write 4logb(X)-1/3logb(y)+2logb(z)as a single logarithm Its log base b.

2. ### College Algebra

I am asked to write a logarithmic expresion as a single logarithm with coefficient 1 and simplify as much as possible. The equation is: 4logbase5Y-3logbase5X+1/2logbase5Z. Could some please help me I am not understanding this

3. ### calculus

Express as a single logarithm ln(a)+1/2ln(b) 2ln4-ln2

4. ### Algebra 2

Can In 5 + log2 10 be written as a single logarithm? Explain.