Math

posted by .

log4x^4 + log4^2 = 3

Solve the logarithmic equation.

  • Math -

    log4x^4 = log4 + 4logx
    log4^2 = 2log4

    log4 + 4logx + 2log4 = 3
    3log4 + 4logx = 3
    4logx = 3(1-log4)

    Now, if we're dealing with base 10, 1 = log10, so 1-log4 = log(10/4) = log(5/2)

    4 logx = 3log(5/2)
    logx = 3/4 log(5/2)

    x = 10^(3/4) * l0^(log 5/2)
    x = 10^3/4 * 5/2
    x = 5/2 10^(3/4)
    x = 5/2 ∜1000

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra II

    Solve, round to four decimal places if necessary: log4(x-9)=2 Answer: x-9=4^2 x-9=16 x=11 log4(z)+log4(z-3)=1 Answer: z+z-3=1 2z=4 z=2 Thanks for checking my work.
  2. Logarithms

    Solve log4 x + log4(x-2)=log4(15) I know how do the example in my book but I don't know what I'm doing wrong here. log4 x + log4(x-2)=log4(15) log4 [x + log4(x-2)]=log4(15) (x^2 + x)=4 x^2 + x-4=0
  3. math

    Solve the equation algebraically. Round the result to three decimal places. log4 x - log4(x-1) = 1/2 I have no idea how to do this. Please help!
  4. Algebra 2

    Simplify: 1. 2log10^5+log10^4 2. 2log3^6-log3^4 3. log4^40-log4^5 4. log4^3-log4^48 I need to see all of the steps. Thanks
  5. Math(Please check)

    solve for x: log4 X - log4 2 = 2 log(2x) = 2 Now what do I do?
  6. calculus

    Please help me solve this equation. log[2](3)+log[2](x)=log[2](5)+log[2](x-2) 1. Solve equation by setting up algebraically. 2. Use appropriate properties of Logarithm to reduce the number of logarithmic terms to only one. 3. Solve …
  7. calculus

    Please help me? ln(x+1)-ln(x-2)=ln(5) 1. Solve equation by setting up algebraically. 2. Use appropriate properties of Logarithm to reduce the number of logarithmic terms to only one. 3. Solve logarithmic equation.
  8. Trig/Pre-Calc

    Could someone please help me on this problem. I'm really confused, and this assignment is due tomorrow. Solve the logarithmic equation algebraically. Approximate the result to three decimal places. log4x-log4(x-1)=1/2 To start off …
  9. math

    solve the equation. log2(x+4)-log4x=2 please show work
  10. Math Algebra 2

    #4. Express the logarithm in terms of log2M and log2N: log2 1/MN #5. Simplify: log4 3 - log4 48 #6. Solve the equation: loga x = 3/2loga 9 + loga 2 #7. Solve the equation: logb (x2 + 7) = 2/3logb 64 #8. Solve the equation: loga (3x …

More Similar Questions