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Algebra
Logarithms
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Solve the equation \(\displaystyle \log_{8}(x + 4119)-\log_{8}(x + 87)=2\).

Using the quotient property of logarithms gives \(\displaystyle \log_{8}\frac{x + 4119}{x + 87} = 2\). Making both sides of the equation exponents on the base \(\displaystyle 8\) gives \(\displaystyle \frac{x + 4119}{x + 87}=64\). Clearing the fractions by multiplying by the LCD gives \(\displaystyle x + 4119=64 x + 5568\). Isolating \(\displaystyle x\) gives \(\displaystyle x = -23\).

Download \(\LaTeX\) 

\begin{question}Solve the equation $\log_{8}(x + 4119)-\log_{8}(x + 87)=2$. 
    \soln{9cm}{Using the quotient property of logarithms gives $\log_{8}\frac{x + 4119}{x + 87} = 2$. Making both sides of the equation exponents on the base $8$ gives $\frac{x + 4119}{x + 87}=64$. Clearing the fractions by multiplying by the LCD gives $x + 4119=64 x + 5568$. Isolating $x$ gives $x = -23$. }

\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_{8}(x + 4119)-\log_{8}(x + 87)=2 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B8%7D%28x%20%2B%204119%29-%5Clog_%7B8%7D%28x%20%2B%2087%29%3D2%20" alt="LaTeX:  \displaystyle \log_{8}(x + 4119)-\log_{8}(x + 87)=2 " data-equation-content=" \displaystyle \log_{8}(x + 4119)-\log_{8}(x + 87)=2 " /> . </p> </p>
HTML for Canvas
<p> <p>Using the quotient property of logarithms gives  <img class="equation_image" title=" \displaystyle \log_{8}\frac{x + 4119}{x + 87} = 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B8%7D%5Cfrac%7Bx%20%2B%204119%7D%7Bx%20%2B%2087%7D%20%3D%202%20" alt="LaTeX:  \displaystyle \log_{8}\frac{x + 4119}{x + 87} = 2 " data-equation-content=" \displaystyle \log_{8}\frac{x + 4119}{x + 87} = 2 " /> . Making both sides of the equation exponents on the base  <img class="equation_image" title=" \displaystyle 8 " src="/equation_images/%20%5Cdisplaystyle%208%20" alt="LaTeX:  \displaystyle 8 " data-equation-content=" \displaystyle 8 " />  gives  <img class="equation_image" title=" \displaystyle \frac{x + 4119}{x + 87}=64 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bx%20%2B%204119%7D%7Bx%20%2B%2087%7D%3D64%20" alt="LaTeX:  \displaystyle \frac{x + 4119}{x + 87}=64 " data-equation-content=" \displaystyle \frac{x + 4119}{x + 87}=64 " /> . Clearing the fractions by multiplying by the LCD gives  <img class="equation_image" title=" \displaystyle x + 4119=64 x + 5568 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%204119%3D64%20x%20%2B%205568%20" alt="LaTeX:  \displaystyle x + 4119=64 x + 5568 " data-equation-content=" \displaystyle x + 4119=64 x + 5568 " /> . 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 = -23 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-23%20" alt="LaTeX:  \displaystyle x = -23 " data-equation-content=" \displaystyle x = -23 " /> . </p> </p>