Question

Having a bit of a problem with this logarithmic equation I will upload a photo

Answer 1

We are asked to solve the equation

`4^(5x-6)=44`

44 cannot be written in index form. So to solve this, we will take logarithm of both sides of the equation

We will have

`\log 4^(5x-6)=\log 44`

Solving for x, we have

`\begin{gathered} \log 4^(5x-6)=\log 44 \\ \\ 5x-6\log 4=\log 44 \\ \\ \text{dividing both sides by log4} \\ \\ 5x-6=(\log 44)/(\log 4) \\ \\ 5x=(\log44)/(\log4)+6 \end{gathered}`

The exact solution becomes

`x=(((\log44)/(\log4)+6))/(5)`

The approximate solution to 4 d.p

`\begin{gathered} x=(((\log44)/(\log4)+6))/(5) \\ \\ x=(((1.64345)/(0.60206)+6))/(5) \\ \\ x=(8.72971)/(5) \\ \\ x=1.7459 \end{gathered}`