MATH $2414$

$7\mathrm{.}3/7\mathrm{.}4$L$-$Other Bases

Solve $lo{g}_2(x-6)+lo{g}_2(x-4)-lo{g}_{2}x=2$

Find the equation of the line tangent to $f(x)=\frac{2^{sin3x}}{sinx}$ at the point $(\frac{}{6},4).$

Find $g^{\text{'}}(x)$ if $g(x)=lo{g}_5(\frac{4}{x^2\sqrt[\phantom{2}]{1-x}})$

Find the equation of the line tangent to $f(x)=(sinx{)}^{2x}$ at the point $(\frac{}{2},1).$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(3-x)7^{(3-x{)}^2}dx$

Solve the initial value problem $\frac{dp}{dh}=kp$ where $p(0)=p_0$

Solve the initial value problem $\frac{dP}{dt}=\frac{3000}{1+0\mathrm{.}25t}$ where $P(0)=1000$