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Algebra
Logarithms
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Solve the equation \(\displaystyle \log_{7}(x + 16802)-\log_{7}(x + 2396)=1\).

Using the quotient property of logarithms gives \(\displaystyle \log_{7}\frac{x + 16802}{x + 2396} = 1\). Making both sides of the equation exponents on the base \(\displaystyle 7\) gives \(\displaystyle \frac{x + 16802}{x + 2396}=7\). Clearing the fractions by multiplying by the LCD gives \(\displaystyle x + 16802=7 x + 16772\). Isolating \(\displaystyle x\) gives \(\displaystyle x = 5\).

Download \(\LaTeX\) 

\begin{question}Solve the equation $\log_{7}(x + 16802)-\log_{7}(x + 2396)=1$. 
    \soln{9cm}{Using the quotient property of logarithms gives $\log_{7}\frac{x + 16802}{x + 2396} = 1$. Making both sides of the equation exponents on the base $7$ gives $\frac{x + 16802}{x + 2396}=7$. Clearing the fractions by multiplying by the LCD gives $x + 16802=7 x + 16772$. Isolating $x$ gives $x = 5$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Solve the equation  <img class="equation_image" title=" \displaystyle \log_{7}(x + 16802)-\log_{7}(x + 2396)=1 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B7%7D%28x%20%2B%2016802%29-%5Clog_%7B7%7D%28x%20%2B%202396%29%3D1%20" alt="LaTeX:  \displaystyle \log_{7}(x + 16802)-\log_{7}(x + 2396)=1 " data-equation-content=" \displaystyle \log_{7}(x + 16802)-\log_{7}(x + 2396)=1 " /> . </p> </p>
HTML for Canvas
<p> <p>Using the quotient property of logarithms gives  <img class="equation_image" title=" \displaystyle \log_{7}\frac{x + 16802}{x + 2396} = 1 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B7%7D%5Cfrac%7Bx%20%2B%2016802%7D%7Bx%20%2B%202396%7D%20%3D%201%20" alt="LaTeX:  \displaystyle \log_{7}\frac{x + 16802}{x + 2396} = 1 " data-equation-content=" \displaystyle \log_{7}\frac{x + 16802}{x + 2396} = 1 " /> . 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 + 16802}{x + 2396}=7 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bx%20%2B%2016802%7D%7Bx%20%2B%202396%7D%3D7%20" alt="LaTeX:  \displaystyle \frac{x + 16802}{x + 2396}=7 " data-equation-content=" \displaystyle \frac{x + 16802}{x + 2396}=7 " /> . Clearing the fractions by multiplying by the LCD gives  <img class="equation_image" title=" \displaystyle x + 16802=7 x + 16772 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2016802%3D7%20x%20%2B%2016772%20" alt="LaTeX:  \displaystyle x + 16802=7 x + 16772 " data-equation-content=" \displaystyle x + 16802=7 x + 16772 " /> . 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 = 5 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%205%20" alt="LaTeX:  \displaystyle x = 5 " data-equation-content=" \displaystyle x = 5 " /> . </p> </p>