(1/8)^k * (1/32768)^(1/3) = 1/8 * (1/32768)^(1/k),then value of k=?
You asked:
Solve the equation \({\left( \frac{1}{8} \right)}^{k} {\left( \frac{1}{32768} \right)}^{\frac{1}{3}} = \frac{1}{8} {\left( \frac{1}{32768} \right)}^{\frac{1}{k}}\) for the variable \(k\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}k &= - \frac{1}{3} + \frac{\sqrt{46}}{3} \approx 1.9274433\\k &= - \frac{1}{3} - \frac{\sqrt{46}}{3} \approx -2.59411\end{aligned}\]