Find the exact value of x Logarithms

LiHJ · Nov 12, 2011

1. The problem statement, all variables and given/known data

Find the exact value of x if:

2. Relevant equations
(3x)^lg3=(4x)^lg4.

3. The attempt at a solution
3^lg3x^lg3=4^lg4x^lg4
(x^lg3)/(x^lg4)=(4^lg4)/(3^lg3)
x^lg3-lg4=(4^lg4)(3^-(lg3))
x^lg(3/4)=(4^lg4)(3^lg(1/3))

Please help me, Im stuck here!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

ehild · Nov 12, 2011

Re: Logarithms

Write both sides of the original equation as power of 10, and compare the exponents (which is the same as taking the lg of both sides)
So you get

lg(3)lg(3x)=lg(4)lg(4x)

that is, (lg3)²+(lg3) lg(x)=(lg4)²+(lg4)lg(x)

Isolate lg(x), use the identity a²-b²=(a-b)(a+b) and simplify. You get lg(x) as the logarithm of a number, from which the exact value of x is found.

ehild

I like Serena · Nov 12, 2011

Re: Logarithms

If x^a=b, then x=b^(1/a).

LiHJ · Nov 13, 2011

Re: Logarithms

Thank you so much echild. The answer is (1/12)

ehild · Nov 13, 2011

Re: Logarithms

Exactly! Well done!

ehild

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Find the exact value of x Logarithms

LiHJ

ehild

I like Serena

LiHJ

ehild

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