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KGB_Maths · Oct 18, 2009, 10:48 AM

How do I solve the equation:

4^Y=8

in a step by step way?
TIA.

Unknown008 · Oct 18, 2009, 10:55 AM

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,

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

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

$y = \frac32$

KGB_Maths · Oct 18, 2009, 11:25 AM

Thank you so much!

Unknown008 · Oct 19, 2009, 09:29 AM

You're welcome! :)