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)

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

(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)

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

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

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

AGK

April 13, 2008 | 12:11 am

(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

alwaysLovely

May 8, 2008 | 7:30 pm

awesome!
Tks for the effort.

Malakia chris Reply:
May 11th, 2011 at 5:12 pm

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ahm97sic

November 8, 2008 | 1:06 am

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,

November 12, 2008 | 10:37 am

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.

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