How do I solve the equation:

4^Y=8

in a step by step way?
TIA.

Ok;

4^y = 8

Insert log on both sides:

log 4^y = log 8

You could have used 'ln' also, but let's do it with log.
Now, you know that you can 'put the index as multiplication' in front of the log like that:

y log 4 = log 8

Then, divide both sides by log 4:

y \cancel{\frac{log 4}{log 4}} = \frac{log 8}{log 4}

y = \frac{log 8}{log 4}

Now, you can enter this in your calculator, or if you want to simplify further,

y = \frac{log 2^3}{log 2^2}

y = \frac{3log 2}{2log 2}

y = \frac32

Thank you so much!

You're welcome! :)