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Algebra
Logarithms
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Solve the equation \(\displaystyle \log_{5}(x + 3128)-\log_{5}(x + 28)=3\).

Using the quotient property of logarithms gives \(\displaystyle \log_{5}\frac{x + 3128}{x + 28} = 3\). Making both sides of the equation exponents on the base \(\displaystyle 5\) gives \(\displaystyle \frac{x + 3128}{x + 28}=125\). Clearing the fractions by multiplying by the LCD gives \(\displaystyle x + 3128=125 x + 3500\). Isolating \(\displaystyle x\) gives \(\displaystyle x = -3\).

Download \(\LaTeX\) 

\begin{question}Solve the equation $\log_{5}(x + 3128)-\log_{5}(x + 28)=3$. 
    \soln{9cm}{Using the quotient property of logarithms gives $\log_{5}\frac{x + 3128}{x + 28} = 3$. Making both sides of the equation exponents on the base $5$ gives $\frac{x + 3128}{x + 28}=125$. Clearing the fractions by multiplying by the LCD gives $x + 3128=125 x + 3500$. Isolating $x$ gives $x = -3$. }

\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_{5}(x + 3128)-\log_{5}(x + 28)=3 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B5%7D%28x%20%2B%203128%29-%5Clog_%7B5%7D%28x%20%2B%2028%29%3D3%20" alt="LaTeX:  \displaystyle \log_{5}(x + 3128)-\log_{5}(x + 28)=3 " data-equation-content=" \displaystyle \log_{5}(x + 3128)-\log_{5}(x + 28)=3 " /> . </p> </p>
HTML for Canvas
<p> <p>Using the quotient property of logarithms gives  <img class="equation_image" title=" \displaystyle \log_{5}\frac{x + 3128}{x + 28} = 3 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B5%7D%5Cfrac%7Bx%20%2B%203128%7D%7Bx%20%2B%2028%7D%20%3D%203%20" alt="LaTeX:  \displaystyle \log_{5}\frac{x + 3128}{x + 28} = 3 " data-equation-content=" \displaystyle \log_{5}\frac{x + 3128}{x + 28} = 3 " /> . Making both sides of the equation exponents on the base  <img class="equation_image" title=" \displaystyle 5 " src="/equation_images/%20%5Cdisplaystyle%205%20" alt="LaTeX:  \displaystyle 5 " data-equation-content=" \displaystyle 5 " />  gives  <img class="equation_image" title=" \displaystyle \frac{x + 3128}{x + 28}=125 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bx%20%2B%203128%7D%7Bx%20%2B%2028%7D%3D125%20" alt="LaTeX:  \displaystyle \frac{x + 3128}{x + 28}=125 " data-equation-content=" \displaystyle \frac{x + 3128}{x + 28}=125 " /> . Clearing the fractions by multiplying by the LCD gives  <img class="equation_image" title=" \displaystyle x + 3128=125 x + 3500 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%203128%3D125%20x%20%2B%203500%20" alt="LaTeX:  \displaystyle x + 3128=125 x + 3500 " data-equation-content=" \displaystyle x + 3128=125 x + 3500 " /> . 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 = -3 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-3%20" alt="LaTeX:  \displaystyle x = -3 " data-equation-content=" \displaystyle x = -3 " /> . </p> </p>