Logarithm Equation Question 3


This is an interesting question which I came across under Additional Mathematics (A-Math):

Find the value of x.

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

Who is courageous to work on this question?

I will respond to this question when someone discusses about this question first :)

Update:

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(Apply Power Law)

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(multiply by 4 on both sides of equal sign)

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(Apply Power Law)
(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(Apply Quotient Law)
(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}
(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(Factorise)

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(log_x8)=0 (NA)or log_x3+1=0

log_x3=-1,3=x^-^1,3=\frac {1}{x},3x=1,x= \frac {1}{3}

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5 Responses to Logarithm Equation Question 3

  1. (log-baseX-root3)(log-baseX-root8)=1.5(log-baseX-1/root2)

    (0.5log-baseX-3)(1.5log-baseX-2)=1.5(log-baseX-2^-0.5)

    [cancel 1.5 from both sides]

    (0.5log-baseX-3)(log-baseX-2)= -0.5(log-baseX-2)

    [cancel 0.5 from both sides]

    (log-baseX-3)(log-baseX-2) + (log-baseX-2)= 0

    (log-baseX-2) (log-baseX-3 + 1) = 0

    therefore,

    (log-baseX-2)=0 or (log-baseX-3 + 1)=0

    X^0= 2 (rejected) (log-baseX-3)= -1
    X^(-1) = 3
    thus X= 1/3

    hope i didnt make any mistakes
    Logarithm rocks! XDD

    Reply

  2. awesome!
    Tks for the effort.

    Reply

    Malakia chris Reply:

    Hie you are just an amazing lady thanks for everything.i will chat with you next time,tell me about your place the temperature & the environment

    Reply

  3. This question is fun. Perhaps, you will like to let your students to try to solve the question.

    Solve the equation

    (2/x)^(log n 4) - (3/x)^(log n 9) = 0

    Regards,

    ahm97sic

    Reply

  4. This is another interesting question. Perhaps, you will like to let your students to try to solve the question.

    Solve (log a X)^(log b X) = X

    where a, b are positive real numbers except 1, leave

    the answer in terms of a and b.

    Regards,

    ahm97sic

    Reply

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