Question

I’m having trouble solving this, and need it explained and answered

Answer 1

We want to solve

`\log _464=m`

Now to solve this, we have to change the logarithmic equation to index equation.

Now, from the logarithmic equation, the base is 4, so this remains the base in the index equation.

So to change to index equation, raise the item outside to the base and equate it to 64.

That is

`\begin{gathered} \log _464=m\text{ to index equation becomes } \\ 4^m=64 \end{gathered}`

Solving the index equation, we have

`\begin{gathered} 4^m=64 \\ 64=4*4*4=4^3 \\ 4^m=64 \\ 4^m=4^3 \\ \text{Canceling the common bases which is 4,} \\ m=3 \end{gathered}`

Hence, the answer is 3