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Algebra
Logarithms
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Solve the equation \(\displaystyle \log_{9}(x + 59032)-\log_{9}(x + 712)=2\).

Using the quotient property of logarithms gives \(\displaystyle \log_{9}\frac{x + 59032}{x + 712} = 2\). Making both sides of the equation exponents on the base \(\displaystyle 9\) gives \(\displaystyle \frac{x + 59032}{x + 712}=81\). Clearing the fractions by multiplying by the LCD gives \(\displaystyle x + 59032=81 x + 57672\). Isolating \(\displaystyle x\) gives \(\displaystyle x = 17\).

Download \(\LaTeX\) 

\begin{question}Solve the equation $\log_{9}(x + 59032)-\log_{9}(x + 712)=2$. 
    \soln{9cm}{Using the quotient property of logarithms gives $\log_{9}\frac{x + 59032}{x + 712} = 2$. Making both sides of the equation exponents on the base $9$ gives $\frac{x + 59032}{x + 712}=81$. Clearing the fractions by multiplying by the LCD gives $x + 59032=81 x + 57672$. Isolating $x$ gives $x = 17$. }

\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_{9}(x + 59032)-\log_{9}(x + 712)=2 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B9%7D%28x%20%2B%2059032%29-%5Clog_%7B9%7D%28x%20%2B%20712%29%3D2%20" alt="LaTeX:  \displaystyle \log_{9}(x + 59032)-\log_{9}(x + 712)=2 " data-equation-content=" \displaystyle \log_{9}(x + 59032)-\log_{9}(x + 712)=2 " /> . </p> </p>
HTML for Canvas
<p> <p>Using the quotient property of logarithms gives  <img class="equation_image" title=" \displaystyle \log_{9}\frac{x + 59032}{x + 712} = 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B9%7D%5Cfrac%7Bx%20%2B%2059032%7D%7Bx%20%2B%20712%7D%20%3D%202%20" alt="LaTeX:  \displaystyle \log_{9}\frac{x + 59032}{x + 712} = 2 " data-equation-content=" \displaystyle \log_{9}\frac{x + 59032}{x + 712} = 2 " /> . Making both sides of the equation exponents on the base  <img class="equation_image" title=" \displaystyle 9 " src="/equation_images/%20%5Cdisplaystyle%209%20" alt="LaTeX:  \displaystyle 9 " data-equation-content=" \displaystyle 9 " />  gives  <img class="equation_image" title=" \displaystyle \frac{x + 59032}{x + 712}=81 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bx%20%2B%2059032%7D%7Bx%20%2B%20712%7D%3D81%20" alt="LaTeX:  \displaystyle \frac{x + 59032}{x + 712}=81 " data-equation-content=" \displaystyle \frac{x + 59032}{x + 712}=81 " /> . Clearing the fractions by multiplying by the LCD gives  <img class="equation_image" title=" \displaystyle x + 59032=81 x + 57672 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2059032%3D81%20x%20%2B%2057672%20" alt="LaTeX:  \displaystyle x + 59032=81 x + 57672 " data-equation-content=" \displaystyle x + 59032=81 x + 57672 " /> . 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 = 17 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%2017%20" alt="LaTeX:  \displaystyle x = 17 " data-equation-content=" \displaystyle x = 17 " /> . </p> </p>