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Algebra
Logarithms
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Solve the equation \(\displaystyle \log_{9}(x + 6586)-\log_{9}(x + 754)=1\).

Using the quotient property of logarithms gives \(\displaystyle \log_{9}\frac{x + 6586}{x + 754} = 1\). Making both sides of the equation exponents on the base \(\displaystyle 9\) gives \(\displaystyle \frac{x + 6586}{x + 754}=9\). Clearing the fractions by multiplying by the LCD gives \(\displaystyle x + 6586=9 x + 6786\). Isolating \(\displaystyle x\) gives \(\displaystyle x = -25\).

Download \(\LaTeX\) 

\begin{question}Solve the equation $\log_{9}(x + 6586)-\log_{9}(x + 754)=1$. 
    \soln{9cm}{Using the quotient property of logarithms gives $\log_{9}\frac{x + 6586}{x + 754} = 1$. Making both sides of the equation exponents on the base $9$ gives $\frac{x + 6586}{x + 754}=9$. Clearing the fractions by multiplying by the LCD gives $x + 6586=9 x + 6786$. Isolating $x$ gives $x = -25$. }

\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 + 6586)-\log_{9}(x + 754)=1 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B9%7D%28x%20%2B%206586%29-%5Clog_%7B9%7D%28x%20%2B%20754%29%3D1%20" alt="LaTeX:  \displaystyle \log_{9}(x + 6586)-\log_{9}(x + 754)=1 " data-equation-content=" \displaystyle \log_{9}(x + 6586)-\log_{9}(x + 754)=1 " /> . </p> </p>
HTML for Canvas
<p> <p>Using the quotient property of logarithms gives  <img class="equation_image" title=" \displaystyle \log_{9}\frac{x + 6586}{x + 754} = 1 " src="/equation_images/%20%5Cdisplaystyle%20%5Clog_%7B9%7D%5Cfrac%7Bx%20%2B%206586%7D%7Bx%20%2B%20754%7D%20%3D%201%20" alt="LaTeX:  \displaystyle \log_{9}\frac{x + 6586}{x + 754} = 1 " data-equation-content=" \displaystyle \log_{9}\frac{x + 6586}{x + 754} = 1 " /> . 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 + 6586}{x + 754}=9 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bx%20%2B%206586%7D%7Bx%20%2B%20754%7D%3D9%20" alt="LaTeX:  \displaystyle \frac{x + 6586}{x + 754}=9 " data-equation-content=" \displaystyle \frac{x + 6586}{x + 754}=9 " /> . Clearing the fractions by multiplying by the LCD gives  <img class="equation_image" title=" \displaystyle x + 6586=9 x + 6786 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%206586%3D9%20x%20%2B%206786%20" alt="LaTeX:  \displaystyle x + 6586=9 x + 6786 " data-equation-content=" \displaystyle x + 6586=9 x + 6786 " /> . 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 = -25 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-25%20" alt="LaTeX:  \displaystyle x = -25 " data-equation-content=" \displaystyle x = -25 " /> . </p> </p>