math

posted by .

write the expression as a sinle logarithm. express powers as factors.

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

Please show work.

  • math -

    You MUST put brackets for the denominators to avoid ambiguity

    I am sure you mean

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

    then
    = lnx - ln(x+1) + (ln(x+1) - lnx - ln( (x+1)(x-1)
    = lnx - ln(x+1) + ln(x+1) + lnx - ln(x+1) - ln(x-1)
    = - 2ln(x+1)

    or

    ln [ (x/(x-1) ((x+1)/x) / ((x+1)x-1))
    = ln (1/(x-1)^2)
    = ln1 - ln(x-1)^2
    = 0 - 2ln(x-1)
    = -2ln(x-1)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math - Write expression as single logarithm

    Write the expression below as a single logarithm. Please show all of your work. ln((x^2 – 1)/(x^2 – 6x + 8)) – ln((x+1)/(x+2))
  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 expression …
  3. precalculus

    write the expression as a sum or difference of logarithms. express powers as factors show all work log4 sqrt pq/7
  4. precalculus

    write the expression below as a single logarithm show work. ln(x-7/x^2+12x+36)-ln(x^2-49/x+6)
  5. math

    change the exponential expression to an equivalent expression involving a logarithm. 8.8=7^x please show work
  6. pre-calculus

    write the expression as a simple logarithm. express powers. In(x/x-5)+In(x+5/x)-In(x^2-25)
  7. college algebra

    write the expression as a single logarithm In(x/x-2)+In(x+2/x)-In(x^2-4) Please show work
  8. math

    use properties of logarithms to condense the loarithmic expression. write expression as a sinle logarithm whose coefficient is 1. where possible evaulate the expression. 1/8[3 In(x+5)-In x-In(x^2-4)] Please show work
  9. Algebre

    Please help I don't understand Contract the expression this is use properties of logarithm to write each expression as a single logarithm with a coefficient of 1. In3-3 In 9 +In 18 In3-2 in (9=6) In 3-2 (In 4 In 8) Thank you so much
  10. algebra

    Write the expression as a sum​ and/or difference of logarithms. Express powers as factors. log3(27x)

More Similar Questions