SOLUTION
We are asked to solve the equation
[tex]4^{5x-6}=44[/tex]44 cannot be written in index form. So to solve this, we will take logarithm of both sides of the equation
We will have
[tex]\log 4^{5x-6}=\log 44[/tex]Solving for x, we have
[tex]\begin{gathered} \log 4^{5x-6}=\log 44 \\ \\ 5x-6\log 4=\log 44 \\ \\ \text{dividing both sides by log4} \\ \\ 5x-6=\frac{\log 44}{\log 4} \\ \\ 5x=\frac{\log44}{\log4}+6 \end{gathered}[/tex]The exact solution becomes
[tex]x=\frac{(\frac{\log44}{\log4}+6)}{5}[/tex]The approximate solution to 4 d.p
[tex]\begin{gathered} x=\frac{(\frac{\log44}{\log4}+6)}{5} \\ \\ x=\frac{(\frac{1.64345}{0.60206}+6)}{5} \\ \\ x=\frac{8.72971}{5} \\ \\ x=1.7459 \end{gathered}[/tex]