(5/3)^-5*(5/3)^11=(5/3)^(8*x)
Find the value of x
You asked:
Solve the equation \[{\left( \frac{5}{3} \right)}^{-5} {\left( \frac{5}{3} \right)}^{11} = {\left( \frac{5}{3} \right)}^{8 x}\] for the unknown \(x\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}x &= \frac{3}{4} = 0.75\\x &= \frac{- 3 \log{\left(5 \right)} + 3 \log{\left(3 \right)}}{4 \left(- \log{\left(5 \right)} + \log{\left(3 \right)}\right)} + \frac{i \pi}{4 \left(- \log{\left(5 \right)} + \log{\left(3 \right)}\right)} \approx 0.75 -1.5375074 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).