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Questions: Algebra BusinessCalculus
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Solve the equation \(\displaystyle \log_{2}(x + 26)-\log_{2}(x + 14)=2\).
Using the quotient property of logarithms gives \(\displaystyle \log_{2}\frac{x + 26}{x + 14} = 2\). Making both sides of the equation exponents on the base \(\displaystyle 2\) gives \(\displaystyle \frac{x + 26}{x + 14}=4\). Clearing the fractions by multiplying by the LCD gives \(\displaystyle x + 26=4 x + 56\). Isolating \(\displaystyle x\) gives \(\displaystyle x = -10\).
\begin{question}Solve the equation $\log_{2}(x + 26)-\log_{2}(x + 14)=2$.
\soln{9cm}{Using the quotient property of logarithms gives $\log_{2}\frac{x + 26}{x + 14} = 2$. Making both sides of the equation exponents on the base $2$ gives $\frac{x + 26}{x + 14}=4$. Clearing the fractions by multiplying by the LCD gives $x + 26=4 x + 56$. Isolating $x$ gives $x = -10$. }
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve the equation <img class="equation_image" title=" \displaystyle \log_{2}(x + 26)-\log_{2}(x + 14)=2 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B2%7D%28x%20%2B%2026%29-%5Clog_%7B2%7D%28x%20%2B%2014%29%3D2%20" alt="LaTeX: \displaystyle \log_{2}(x + 26)-\log_{2}(x + 14)=2 " data-equation-content=" \displaystyle \log_{2}(x + 26)-\log_{2}(x + 14)=2 " /> . </p> </p><p> <p>Using the quotient property of logarithms gives <img class="equation_image" title=" \displaystyle \log_{2}\frac{x + 26}{x + 14} = 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B2%7D%5Cfrac%7Bx%20%2B%2026%7D%7Bx%20%2B%2014%7D%20%3D%202%20" alt="LaTeX: \displaystyle \log_{2}\frac{x + 26}{x + 14} = 2 " data-equation-content=" \displaystyle \log_{2}\frac{x + 26}{x + 14} = 2 " /> . Making both sides of the equation exponents on the base <img class="equation_image" title=" \displaystyle 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX: \displaystyle 2 " data-equation-content=" \displaystyle 2 " /> gives <img class="equation_image" title=" \displaystyle \frac{x + 26}{x + 14}=4 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bx%20%2B%2026%7D%7Bx%20%2B%2014%7D%3D4%20" alt="LaTeX: \displaystyle \frac{x + 26}{x + 14}=4 " data-equation-content=" \displaystyle \frac{x + 26}{x + 14}=4 " /> . Clearing the fractions by multiplying by the LCD gives <img class="equation_image" title=" \displaystyle x + 26=4 x + 56 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2026%3D4%20x%20%2B%2056%20" alt="LaTeX: \displaystyle x + 26=4 x + 56 " data-equation-content=" \displaystyle x + 26=4 x + 56 " /> . Isolating <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle x = -10 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-10%20" alt="LaTeX: \displaystyle x = -10 " data-equation-content=" \displaystyle x = -10 " /> . </p> </p>