Hello :P
How do i simplify this?:
log4(16)*log4(4)
And this:
f(x)=xsin^(-1)x
thanks...!
Welcome to MHF!
2 rules very handy for this type of problem are;
$\displaystyle log_{a}a=1$
$\displaystyle log_{a}(b^c)=c \cdot log_{a}b$
So we know $\displaystyle log_{4}4 = 1$
and we can simplify $\displaystyle log_{4}16=log_{4}(4^2)=2log_{4}4$.
Therefore,
$\displaystyle (log_{4}16)(log_{4}4)$
$\displaystyle =(log_{4}(4^2))(1)$
$\displaystyle =(2 \cdot log_{4}4)(1)$
$\displaystyle =(2)(1)(1)$
$\displaystyle =2$
Does this help?
It's not so much that it can't be figured out, there is just no way to simplify that expression further.
Keep in mind that differentiation and algebraic simplification are two very different things!
Differentiating will bring out an entirely new function that is not at all equivalent to the original.
No, no, because simplification is essentially rewriting a function such that it is equivalent to the original function and so it looks nicer and is easier to work with.
If you differentiate, you lose that equivalency to the original function; so nothing to do with differentiation can be considered an algebraic simplification. Sure you *might* be able to simplify the derivative, but it would not be a simplification of $\displaystyle (x)sin^{-1}(x)$.