91Ó°ÊÓ

Solve the given problem for \(x,\) if possible. If a problem cannot be solved, explain why. $$ 5^{x}=0.2 $$

In exercises \(13-20\), factor each function completely. $$ x(z)=3 z^{3}+6 z^{2}-24 z $$

Evaluate the described mathematical statement, or determine how the described changes affect other variables in the statement as appropriate. The Reynold's number, which helps identify whether or not a fluid flow is turbulent, is given by \(\mathrm{Re}=\frac{\rho \mathrm{uD}}{\mu} .\) If \(\rho, \mathrm{u},\) and \(\mathrm{D}\) are held constant while \(\mu\) increases, does Re increase, decrease, or stay the same?

In exercises \(11-17,\) simplify the given term and write your answer without negative exponents. $$ \frac{e^{x^{2}-1}}{e^{x+1}} $$

Solve the given problem for \(x,\) if possible. If a problem cannot be solved, explain why. $$ 5^{x}=1 $$

In exercises \(18-20,\) simplify and write the given term in exponential form. $$ \frac{4 x-1}{\sqrt[3]{(3 x+2)^{2}}} $$

In exercises \(13-20\), factor each function completely. $$ y(x)=x^{3}+8 $$

In exercises \(18-25,\) solve the given problem for \(X\). $$ 3^{x-6}=2 $$

Evaluate the described mathematical statement, or determine how the described changes affect other variables in the statement as appropriate. Consider a square-based box whose height is twice the length of the base of the side. If the length of the square base is \(3 \mathrm{ft},\) what is the volume of the box? (Don't forget your units!)

In exercises \(18-20,\) simplify and write the given term in exponential form. $$ \sqrt[3]{\left(\frac{e^{4 \theta-6} y^{2}}{e^{\theta} y^{-4}}\right)} $$