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Questions: Algebra BusinessCalculus
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Solve the equation \(\displaystyle \log_{7}(x + 16792)-\log_{7}(x + 34)=3\).
Using the quotient property of logarithms gives \(\displaystyle \log_{7}\frac{x + 16792}{x + 34} = 3\). Making both sides of the equation exponents on the base \(\displaystyle 7\) gives \(\displaystyle \frac{x + 16792}{x + 34}=343\). Clearing the fractions by multiplying by the LCD gives \(\displaystyle x + 16792=343 x + 11662\). Isolating \(\displaystyle x\) gives \(\displaystyle x = 15\).
\begin{question}Solve the equation $\log_{7}(x + 16792)-\log_{7}(x + 34)=3$.
\soln{9cm}{Using the quotient property of logarithms gives $\log_{7}\frac{x + 16792}{x + 34} = 3$. Making both sides of the equation exponents on the base $7$ gives $\frac{x + 16792}{x + 34}=343$. Clearing the fractions by multiplying by the LCD gives $x + 16792=343 x + 11662$. Isolating $x$ gives $x = 15$. }
\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_{7}(x + 16792)-\log_{7}(x + 34)=3 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B7%7D%28x%20%2B%2016792%29-%5Clog_%7B7%7D%28x%20%2B%2034%29%3D3%20" alt="LaTeX: \displaystyle \log_{7}(x + 16792)-\log_{7}(x + 34)=3 " data-equation-content=" \displaystyle \log_{7}(x + 16792)-\log_{7}(x + 34)=3 " /> . </p> </p><p> <p>Using the quotient property of logarithms gives <img class="equation_image" title=" \displaystyle \log_{7}\frac{x + 16792}{x + 34} = 3 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B7%7D%5Cfrac%7Bx%20%2B%2016792%7D%7Bx%20%2B%2034%7D%20%3D%203%20" alt="LaTeX: \displaystyle \log_{7}\frac{x + 16792}{x + 34} = 3 " data-equation-content=" \displaystyle \log_{7}\frac{x + 16792}{x + 34} = 3 " /> . Making both sides of the equation exponents on the base <img class="equation_image" title=" \displaystyle 7 " src="/equation_images/%20%5Cdisplaystyle%207%20" alt="LaTeX: \displaystyle 7 " data-equation-content=" \displaystyle 7 " /> gives <img class="equation_image" title=" \displaystyle \frac{x + 16792}{x + 34}=343 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bx%20%2B%2016792%7D%7Bx%20%2B%2034%7D%3D343%20" alt="LaTeX: \displaystyle \frac{x + 16792}{x + 34}=343 " data-equation-content=" \displaystyle \frac{x + 16792}{x + 34}=343 " /> . Clearing the fractions by multiplying by the LCD gives <img class="equation_image" title=" \displaystyle x + 16792=343 x + 11662 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2016792%3D343%20x%20%2B%2011662%20" alt="LaTeX: \displaystyle x + 16792=343 x + 11662 " data-equation-content=" \displaystyle x + 16792=343 x + 11662 " /> . 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 = 15 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%2015%20" alt="LaTeX: \displaystyle x = 15 " data-equation-content=" \displaystyle x = 15 " /> . </p> </p>