I figure there are some smart people here at ECF that probably know what I'm doing wrong, I'm finding the derivative of some log functions, and I'm a but rusty on my log rules and something is confusing me:
The power rule of logarithm states that:
ln (x^y) = y ln (x)
Which seems to be true when only using constants, for example: ln(2^8) = 8ln(2)
But doesn't seem to be true when using a variable, for example: ln(x^2) does not = 2ln(x)
Is there a different rule that is applied when using variables, or is there something else I'm missing here?
I'm supposed to be finding the derivative of ln(x)/ln(x^2) without using the product or quotient rule of differentiation so I assume I'm supposed to be changing the function somehow but I'm not sure exactly how. I've been looking around online for awhile at the various math sites and can't seem to find what I'm looking for.
Any help would be greatly appreciated! Thanks!
The power rule of logarithm states that:
ln (x^y) = y ln (x)
Which seems to be true when only using constants, for example: ln(2^8) = 8ln(2)
But doesn't seem to be true when using a variable, for example: ln(x^2) does not = 2ln(x)
Is there a different rule that is applied when using variables, or is there something else I'm missing here?
I'm supposed to be finding the derivative of ln(x)/ln(x^2) without using the product or quotient rule of differentiation so I assume I'm supposed to be changing the function somehow but I'm not sure exactly how. I've been looking around online for awhile at the various math sites and can't seem to find what I'm looking for.
Any help would be greatly appreciated! Thanks!
