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Algebra
Logarithms
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Solve the equation \(\displaystyle \log_{6}(x + 1276)-\log_{6}(x + 16)=2\).

Using the quotient property of logarithms gives \(\displaystyle \log_{6}\frac{x + 1276}{x + 16} = 2\). Making both sides of the equation exponents on the base \(\displaystyle 6\) gives \(\displaystyle \frac{x + 1276}{x + 16}=36\). Clearing the fractions by multiplying by the LCD gives \(\displaystyle x + 1276=36 x + 576\). Isolating \(\displaystyle x\) gives \(\displaystyle x = 20\).

Download \(\LaTeX\) 

\begin{question}Solve the equation $\log_{6}(x + 1276)-\log_{6}(x + 16)=2$. 
    \soln{9cm}{Using the quotient property of logarithms gives $\log_{6}\frac{x + 1276}{x + 16} = 2$. Making both sides of the equation exponents on the base $6$ gives $\frac{x + 1276}{x + 16}=36$. Clearing the fractions by multiplying by the LCD gives $x + 1276=36 x + 576$. Isolating $x$ gives $x = 20$. }

\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_{6}(x + 1276)-\log_{6}(x + 16)=2 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B6%7D%28x%20%2B%201276%29-%5Clog_%7B6%7D%28x%20%2B%2016%29%3D2%20" alt="LaTeX:  \displaystyle \log_{6}(x + 1276)-\log_{6}(x + 16)=2 " data-equation-content=" \displaystyle \log_{6}(x + 1276)-\log_{6}(x + 16)=2 " /> . </p> </p>
HTML for Canvas
<p> <p>Using the quotient property of logarithms gives  <img class="equation_image" title=" \displaystyle \log_{6}\frac{x + 1276}{x + 16} = 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B6%7D%5Cfrac%7Bx%20%2B%201276%7D%7Bx%20%2B%2016%7D%20%3D%202%20" alt="LaTeX:  \displaystyle \log_{6}\frac{x + 1276}{x + 16} = 2 " data-equation-content=" \displaystyle \log_{6}\frac{x + 1276}{x + 16} = 2 " /> . Making both sides of the equation exponents on the base  <img class="equation_image" title=" \displaystyle 6 " src="/equation_images/%20%5Cdisplaystyle%206%20" alt="LaTeX:  \displaystyle 6 " data-equation-content=" \displaystyle 6 " />  gives  <img class="equation_image" title=" \displaystyle \frac{x + 1276}{x + 16}=36 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bx%20%2B%201276%7D%7Bx%20%2B%2016%7D%3D36%20" alt="LaTeX:  \displaystyle \frac{x + 1276}{x + 16}=36 " data-equation-content=" \displaystyle \frac{x + 1276}{x + 16}=36 " /> . Clearing the fractions by multiplying by the LCD gives  <img class="equation_image" title=" \displaystyle x + 1276=36 x + 576 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%201276%3D36%20x%20%2B%20576%20" alt="LaTeX:  \displaystyle x + 1276=36 x + 576 " data-equation-content=" \displaystyle x + 1276=36 x + 576 " /> . 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 = 20 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%2020%20" alt="LaTeX:  \displaystyle x = 20 " data-equation-content=" \displaystyle x = 20 " /> . </p> </p>