Logarithm Q: 2logx - 1/2log(x-1) + 3log(x+2) = 0

Spoon-

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I can't solve this, please help.

2logx - 1/2log(x-1) + 3log(x+2) = 0
 
Re: Logarithm Question

Your question reduces to \(\displaystyle \frac{{x^2 \left( {x + 2} \right)^3 }}{{\sqrt {x - 1} }} = 1\).
Do you know why?
 
Re: Logarithm Question

Just to add, reviewing these may help:

\(\displaystyle nlog_{a}b = log_{a}b^{n}\)

\(\displaystyle a^{\frac{m}{n}} = \sqrt[m]{a^{n}} = (\sqrt[m]{a})^{n}\)

\(\displaystyle log_{a}b + log_{a}c = log_{a}(b \cdot c)\)

\(\displaystyle log_{a}b - log_{a}c = log_{a}\left(\frac{b}{c}\right)\)

\(\displaystyle log_{a}b = c \quad \mbox{is the same thing as} \quad a^{c} = b\)
 
Spoon- said:
I can't solve this, please help.

2logx - 1/2log(x-1) + 3log(x+2) = 0

Did you really want to solve for 'x'?

What methods have learned to solve non-linear (beyond quadratic) equations?
 
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