Algebra

posted by .

Solve the equation.
2log3 y = log3 4+ log3 (y+8)

Here's what ive got
take out the logs and say y^2= 4+ y +8
which simplifies to (y^2)-y=12
how do i simplfy the y?

  • Algebra -

    note that you cannot simplify the right side equation log3 (4) + log3 (y+8) , by 4 + y + 8 ... they should be multiplied. recall some laws of exponents; if we are add terms of the same base, for example
    log 3 + log 5
    this simplifies to
    log(3*5) or log 15
    going back to the problem, the equation simplifies to
    2log3 y = log3 4 + log3 (y+8)
    log3 (y^2) = log3 (4*(y+8))
    log3 (y^2) = log3 (4y + 32)
    cancelling out the log3,
    y^2 = 4y + 32
    y^2 - 4y - 32 = 0
    this is a quadratic equation. since it's factorable, let's just factor this one:
    (y - 8)(y + 4) = 0
    y = 8 and y = -4
    note that y = -4 is extraneous, since if we substitute this back to the original, and take its log:
    left side: 2log3 (-4) = undefined
    thus,
    y = 8

    hope this helps~ :)

  • Algebra -

    Jai, your a life saver! you explained everything perfectly! thank you sooo much!

    that helped a ton, thanks! : )

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math - logs

    log_3(2x - 1) = 2, Find x. Here's what I've done: log_3(2x) * log_3(1) = 2 log2x/log3 * log1/log3 = 2 trial and error... log2 (2*1.4)/log3 * 0 = 2.03... x = 1.4 I think I did it wrong because anything that multiplies with 0 gives you …
  2. Math

    (I have two questions) 1. Solve for x without a calculator: log3(x^2)=2log3(4)-4log3(5) This is what I have so far: 2log3(x)=log3(4^2)-log3(5^4) 2log3(x)=log3(16/625) ...and now I'm stuck. 2. Simplify: 2log4(9)-2log3 <--how do you …
  3. Precalculus

    Please help me with these questions ASAP!! Suppose that f(x)=log3(x-1) a)If f(6)=1.4 and f(8)=1.7,then evaluate log3(35) and log3(7/5). b)If f(3)=0.6, find log9(2).
  4. Pre-Cal

    1) Solve the equation exactly for x: log3 x - log3(x-3) = 2 I got 1 as an answer. Is this correct?
  5. Algebra 1

    Lesson 3 Assignment .Explain the differences between solving these two equations: By steps log3(x - 1) = 4 AND log3(x - 1) = log3^4
  6. ALGEBRA 1

    Lesson 3 Assignment .Explain the differences between solving these two equations: By steps log3(x - 1) = 4 AND log3(x - 1) = log3^4
  7. Math

    Solve the logarithmic equation. Express your solutions in exact form only. Please show all of your work. log3(x+2) + log3(x+8) – 2 = log3(x+3)
  8. Algebra (logs)

    Please help, I need help on these two problems. Solve the equation. log3(x − 16) = log3(9x) e^1 + ln(7) It appears on the homework that the ln(7) is written like this ^ln(7) but I am still stuck on it. Thanks!
  9. Math

    Logarithms 3^x-2=18 Work log(3^x-2)=log18 (x-2)log3=log18 xlog3-2log3=log18 x=log3/(log9-log18) e^3x+1=10 lne^3x+1=ln10 3x+1=ln10 I'm stuck here 8^x=5^2x-1 xlog8=(2x-1)log5 xlog8=2xlog5-log5 x=log10/(log5-log8) Are these right?
  10. Math

    I need help, please find the exact value of 2log3 27+log3 (1/3)-log3 3^1/2 many thanks

More Similar Questions