left f(x)=2^(sin(x))Find f'(x)

Solve for X ${\displaystyle \log X=4}$

Find the exponential function whose grapgh is given

I am new to logarithms and I am having trouble with this logarithm system.
${\displaystyle {\log }_9\left(x\right)+{\log }_y\left(8\right)=2}$
${\displaystyle {\log }_x\left(9\right)+{\log }_8\left(y\right)=\frac{8}{3}}$
A step-by-step procedure would be highly appreciated.
Thanks in advance.

8x^3−48x^2+96x−64

Find the complete factorization of $P(x)=x^4-2x^3+5x^2-8x+4$.

Expand Q to prove that the polynomials P and Q are the same.
${\displaystyle P\left(x\right)=3x^4-5x^3+x^2-3x+5}$
${\displaystyle Q\left(x\right)=(((3x-5)x+1)x-3)x+5}$
Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial ${\displaystyle R\left(x\right)=x^5-2x^4+3x^3-2x^2+3x+4}$ in "nested" form, like the polynomial Q. Use the nested form to find R(3) in your head.
Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?