How do i solve this logarithmic expression??-10 points!?

Given that log(3)4 =p and log (3)5 =q , find the value of x if log(3)x= 2p-q+2

Ive gotten this far. 2log(3)4 - log(3)5 +2 ===> log(3)16 - log(3)5 +2 ====> log(3)16/log(3)5 +2===> 16/5 +2 , now what is the value of x? And is there an error? The answer is 144/5. Please explain

Plus

If log(5)p - log(5)4 =2 find the value of p, do i solve like this? P/4 = 2 then p=8 ... But the answer sheet says im wrong. Please explain my errors...

Lastly, if log(2)x^3 +log(2)x=8, find the value of x====> x^3 +x-8=0 .... How do i solve thhis? Please explain with step by step method

Please answeer all 3 for your 10 point best answer!!

3 Answers

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  • iceman
    Lv 7
    9 years ago
    Favorite Answer

    log3(x) = 2p - q + 2

    log3(x) = 2log3(4) - log3(5) + 2

    log3(x) = log3[16/5] + 2

    x = 3^ {log3[16/5] + 2}

    x = 16/5 * 3^2

    x = 144/5

    log5(p) - log5(4) =2

    log5(p/4) = 2

    p/4 = 5^2 = 25

    p = 4*25 = 100

    log2(x^3) +log2(x) = 8

    log2(x^3 * x) = 8

    log2(x^4) = 8

    x^4 = 2^8 = 256

    x^4 = 4^4

    x = 4

    Regards.

  • 9 years ago

    Given that log(3)4 =p and log (3)5 =q ,

    find the value of x if log(3)x= 2p-q+2

    log(3)x = 2p-q+2 = 2[log(3)4] -log(3)5 +2 =

    = log(3)[4^2/5] +2 = log(3)3.2 + 2 =

    = log(3.2) / log3 +2 = 0.50515/0.477122 +2 =

    log(3)x = 1.05875 +2 = 3.05875

    logx/log3 = 3.05875,

    logx = 3.05875(log3) = log(3^3.05875)

    SO,

    x = 3^3.05875 = 28.8 = 144/5 >=================< ANSWER

    2.

    log(5)p - log(5)4 = 2 = log(5)25

    log(5)[p/4] = log(5)25

    p/4 = 25.

    SO,

    p = 4*25 = 100 >==========================< ANSWER

    3.

    log(2)x^3 +log(2)x = 8 = log(2)256

    log(2)[x^3*x] = log(2)256

    x^4 = 256 = 4^4

    So,

    x = 4 >=====================< ANSWER

  • nancey
    Lv 4
    4 years ago

    permit log okay to the backside 2 = a. So ok = 2^a permit log okay to the backside 4 = b So ok = 4^b = (2^2)^b = 2^(2b) for this reason 2^a = 2^(2b) and so a = 2b on condition that b = 2 + a hence a = 2(2 + a), a = -4, b = -2, ok = 4^(-2) = a million / 4^2 = a million/sixteen

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