I have the expression . In simplifying the first term I need to get rid of the square root and change the coefficient of 4 to an exponent. So if I get rid of the square root first that would be so when I now change the coefficient of 4 to an exponent, shouldnt the term be ? It seems that the actual answer is but according to the properties of logarithms I dont understand why. The properties say that and so why is the simplification of the term and not ?
In other words if then why am I simply multiplying the exponent of 1/2 in by 4 instead of raising it to a power of 4?
Hello mgrade2000
You're asking lots of questions here. Let me see if I can answer them one at a time.Correct!Yes. It is.so when I now change the coefficient of 4 to an exponent, shouldnt the term be ?I think that at the heart of your confusion is that you're not sure what means. It means:It seems that the actual answer is but according to the properties of logarithms I dont understand why.which is the same as:Notice that it isn't:That would be:which is something different altogether.
Can you see now that these are the same thing?The properties say that and so why is the simplification of the term and not ?
See above!In other words if then why am I simply multiplying the exponent of 1/2 in by 4 instead of raising it to a power of 4?
Grandad