When bases are not the same, we can solve an exponential equation by taking logarithms on each side of the equation.
m=n⇔log(m)=log(n)
Note that in order to take their logarithms, both m and n must be positive numbers. Let's now solve our equation.
The exact solution is x=31log6(7)+3. To find an approximate solution to three decimal places, we will use a calculator.
x=31log6(7)+3Useacalculatorx≈3.362