Advanced Functions/ Precalculus Log

1. Evaluate 4^(log base4 64) + 10^(log100)

2. Write 1+log(base2)x^3 as a single logarithm

3. Write log(base b)√(x^3 y z^6)

4. Solve log(base 2)x-log(base 2)6=log(base 2)5+2log(base 2)3

5. Solve 3^(2x) = 9(81^x)

6. Solve 3^(2x)=7^(3x-1). Round answer to two decimal places.

7. Solve log(x+3) + log(x-2) = log(3x+2)

  1. 👍 0
  2. 👎 0
  3. 👁 113
asked by Jessie
  1. By definition, blogbN = N

    #1. 64+100 = 164
    #2. 1 = log2, so you have
    log2+log(x^3) = log(2x^3)
    #3. 1/2 (3logx + logy + 6logz)
    #4. supressing the "base 2" for readability, we have

    logx - log6 = log5+2log3
    log(x/6) = log(5*3^2)
    x/6 = 45
    x = 270
    Actually, since all the logs are the same base, the base doesn't really matter.

    #5. Since 9=3^2 and 81=3^4, you have

    3^(2x) = 3^2 * 3^4x
    3^2x = 3^(2+4x)
    2x = 2+4x
    x = -1
    Check: 3^-2 = 1/9
    9(81^-1) = 9/81 = 1/9

    #6.
    3^(2x) = 7^(3x-1)
    2x log3 = (3x-1) log7
    2x/(3x-1) = log7/log3
    x = 0.53

    #7.
    log (x+3)(x-2) = log (3x+2)
    (x+3)(x-2) = (3x+2)
    x = -2 or 4

    1. 👍 0
    2. 👎 0
    posted by Steve
  2. Thanks a lot!

    1. 👍 0
    2. 👎 0
    posted by Jessie
  3. #7. Actually, x = -2 needs to be discarded, since log(x-2) is not defined there.

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

    asked by kevin on June 12, 2011
  2. math

    write as a single logarithm: -2logbase3(1/x)+(1/3)logbase3(square root of x) please show the steps to solving this. thanx. remember that 1 log (AxB) = log A + Log B (same base) 2 log (A/B) = log A - log B 3 log A^n = n log A use

    asked by michelle on February 25, 2007
  3. Maths

    Log base2(x+2)+log base4(y+10)=2 Log base4(x+2)+log base2(y+10)=5/2 Solve simultaneously

    asked by Rhonick on May 8, 2018
  4. 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

    asked by michelle on March 13, 2007
  5. math

    Logarithm!!! Select all of the following that are true statements: (a) log(2x) = log(2) + log(x) (b) log(3x) = 3 log(x) (c) log(12y) = 2 log(2) + log(3y) (d) log(5y) = log(20y) – log(4) (e) log(x) = log(5x) – log(5) (f) ln(25)

    asked by Simon on April 16, 2010
  6. Precalculus

    Evaluate log(base4)8 + log(base4)(1/8 log(base4)=(8x1/8) =1 I got 1 but the back of the book says 0...?

    asked by Matthew on January 30, 2012
  7. Algebra

    How would I write 1-2log(7)x as a single logarithm Choices: log(7) x^2/7 log(7) 7x^2 log(7) 7/x^2 log (7) x^2 Thank you

    asked by Jesse on November 15, 2010
  8. Precalculus-Verify

    log(base2)x-log(base2)6= log(base2)5+ 2log(base2)3 log(x/6)=3log15 (x/6)=15^3 6*(x/6)=15^3*6 x=15^3*6 =20,250 Answer is 270.... What did I do wrong...

    asked by Melinda on January 30, 2012
  9. Math (pre-celc 12)

    Write the expression as a single logarithm: 3log(a)-log(b)-(1/2)log(c) I want to check my answer. I got log(a^3/bc^(1/2))

    asked by Jana on May 30, 2016
  10. college algebra

    Write expression as one logarithm and simplify if appropriate. log 3√x + log x^4 - log x^3 4 log (x+3) - 5 log (x^2+4) + 1/3 log y I have these who problems but I don't know where to start. HELP Please.

    asked by Deb on April 17, 2013

More Similar Questions