J jimmypop New member Joined Apr 26, 2009 Messages 16 May 4, 2009 #1 Here is what I got so far, but I'm not sure where to go from here? log^((x^2) - log (x+25))=2 log(x^2/x+25)=2 x^2/x+25=10^2 Where do I go from here???
Here is what I got so far, but I'm not sure where to go from here? log^((x^2) - log (x+25))=2 log(x^2/x+25)=2 x^2/x+25=10^2 Where do I go from here???
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 May 4, 2009 #2 Hello, jimmypop! \(\displaystyle \text{Solve: }\;2\log x - 2 \:=\:\log(x+25)\) Click to expand... Note that \(\displaystyle x\) must be positive. \(\displaystyle \text{We have: }\;\log(x^2) - \log(x+25) \:=\:2 \quad\Rightarrow\quad \log\left(\frac{x^2}{x+25}\right) \:=\:\log(10^2)\) \(\displaystyle \text{"Un-log" both sides: }\;\frac{x^2}{x + 25} \:=\:100 \quad\Rightarrow\quad x^2 \:=\:100(x + 25)\) . . \(\displaystyle x^2 \:=\:100x + 2500 \quad\Rightarrow\quad x^2 - 100 - 2500 \:=\:0\) \(\displaystyle \text{Quadratic Formula: }x \:=\:\frac{100 \pm \sqrt{20000}}{2} \:=\:50(1 \pm\sqrt{2})\) \(\displaystyle \text{Therefore: }\;x \:=\:50(1 + \sqrt{2})\)
Hello, jimmypop! \(\displaystyle \text{Solve: }\;2\log x - 2 \:=\:\log(x+25)\) Click to expand... Note that \(\displaystyle x\) must be positive. \(\displaystyle \text{We have: }\;\log(x^2) - \log(x+25) \:=\:2 \quad\Rightarrow\quad \log\left(\frac{x^2}{x+25}\right) \:=\:\log(10^2)\) \(\displaystyle \text{"Un-log" both sides: }\;\frac{x^2}{x + 25} \:=\:100 \quad\Rightarrow\quad x^2 \:=\:100(x + 25)\) . . \(\displaystyle x^2 \:=\:100x + 2500 \quad\Rightarrow\quad x^2 - 100 - 2500 \:=\:0\) \(\displaystyle \text{Quadratic Formula: }x \:=\:\frac{100 \pm \sqrt{20000}}{2} \:=\:50(1 \pm\sqrt{2})\) \(\displaystyle \text{Therefore: }\;x \:=\:50(1 + \sqrt{2})\)
