1. 2ln(3x) = 8
2. Logx + log (x + 15) = 2
3. Ln (x - 4) - ln (x + 1) = ln 6
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1. 2ln(3x) = 8
2. Logx + log (x + 15) = 2
3. Ln (x - 4) - ln (x + 1) = ln 6
$\displaystyle 2\ln \left( {3x} \right) = 8 \Leftrightarrow \ln \left( {3x} \right) = 4 \Leftrightarrow 3x = {e^4} \Leftrightarrow x = \frac{{{e^4}}}{3}.$Quote:
Originally Posted by garbles
Thanks just need the last 2
$\displaystyle \underbrace {\ln \left( {x - 4} \right) - \ln \left( {x + 1} \right)}_{\ln a - \ln b = \ln \frac{a}{b}} = \ln 6 \Leftrightarrow \ln \frac{{x - 4}}{{x + 1}} = \ln 6 \Leftrightarrow$Quote:
Originally Posted by garbles
$\displaystyle \Leftrightarrow \frac{{x - 4}}{{x + 1}} = 6 \Leftrightarrow x - 4 = 6\left( {x + 1} \right) \Leftrightarrow 5x = - 10 \Leftrightarrow x = - 2.$
What is a basis of these logarithms?Quote:
Originally Posted by garbles
$\displaystyle {\log _{\color{red}{?}}}x + {\log _{\color{red}{?}}}\left( {x + 15} \right) = 2.$
It doesn't sayQuote:
Originally Posted by DeMath
I'd just assume base 10.Quote:
Originally Posted by DeMath
So, $\displaystyle log_{10}(x(x+15))=log_{10}(x^{2}+15x)$
Thus, $\displaystyle 10^{2}=x^{2}+15x$ and $\displaystyle x^{2}+15x-100=0$ becomes the equation you have to solve for.
You will want to keep the non-negative answer.
Quote:
Originally Posted by garbles
$\displaystyle \log{x}+\log{(x+15)}=2$
$\displaystyle \log{(x(x+15))}=2$
$\displaystyle \log{(x^2+15x)}=2$
$\displaystyle x^2+15x=10^2$
$\displaystyle x^2+15x-100=0$
$\displaystyle (x+20)(x-5)=0$
x=5 not -20 since $\displaystyle \log{-20}$ is undefined
