if 2^a= 3 , 5^b=2 and abc=1 then find 3^c
You asked:
Given the following equations: \[\begin{aligned}{2}^{a} &= 3\\ {5}^{b} &= 2\\ a b c &= 1\end{aligned}\] Evaluate \({3}^{c}\).
MathBot Answer:
The system of equations has one solution.
\[a = \frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}, b = \frac{\log{\left(2 \right)}}{\log{\left(5 \right)}}, c = \frac{\log{\left(5 \right)}}{\log{\left(3 \right)}}\]
By substituting these values into the expression, we find that: $$\begin{aligned}3^{c} &= 5\end{aligned}$$