- 2 log 𝑧 − log(7𝑧 − 1) = 0

asked by guest
on Nov 18, 2024 at 10:40 pm



You asked:

Solve the equation \(-\left( 2 \cdot \log\left( z \right) \right) - \log\left( 7 z - 1 \right) = 0\) for the variable \(z\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}z &= \frac{1}{21} + \sqrt[3]{\frac{1325}{18522} + \frac{\sqrt{3981}}{882}} + \frac{1}{441 \sqrt[3]{\frac{1325}{18522} + \frac{\sqrt{3981}}{882}}} \approx 0.57497572\\z &= - \frac{\sqrt[3]{\frac{\sqrt{3981}}{882} + \frac{1325}{18522}}}{2} - \frac{1}{882 \sqrt[3]{\frac{\sqrt{3981}}{882} + \frac{1325}{18522}}} + \frac{1}{21} + i \left(- \frac{\sqrt{3}}{882 \sqrt[3]{\frac{\sqrt{3981}}{882} + \frac{1325}{18522}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{3981}}{882} + \frac{1325}{18522}}}{2}\right) \approx -0.21605929 + 0.44919492 i\\z &= - \frac{\sqrt[3]{\frac{\sqrt{3981}}{882} + \frac{1325}{18522}}}{2} - \frac{1}{882 \sqrt[3]{\frac{\sqrt{3981}}{882} + \frac{1325}{18522}}} + \frac{1}{21} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{3981}}{882} + \frac{1325}{18522}}}{2} + \frac{\sqrt{3}}{882 \sqrt[3]{\frac{\sqrt{3981}}{882} + \frac{1325}{18522}}}\right) \approx -0.21605929 -0.44919492 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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