Question
Felect the correct next step. Find the solution. \[ \begin{array}{l}\log _{4}\left(\frac{8 x}{x-7}\right)=3 \\ \frac{8 x}{x-7}=4^{3} \quad \frac{8 x}{x-7}=3 \cdot 4 \quad \frac{8 x}{x-7}=3^{4} \\ \end{array} \]
Ask by Tucker Hall. in the United States
Jan 24,2025
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Answer
The solution is \( x = 8 \).
Solution
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To find the solution to the equation \(\log_{4}\left(\frac{8 x}{x-7}\right)=3\), you correctly set the equation in the exponential form. Therefore, the next step is: \(\frac{8 x}{x-7} = 4^{3}\) Now, with \(4^{3}=64\), you can proceed to solve the equation \(\frac{8 x}{x-7}=64\) for \(x\). Next, adjust the equation to eliminate the fraction: \(8x = 64(x - 7)\) Expanding and then simplifying will lead you to find the value of \(x\). Happy solving!