Problem 1

In Exercises \(1-4\) use the properties of exponents to simplify the expression. (a) \(\left(e^{3}\right)\left(e^{4}\right)\) (b) \(\left(e^{3}\right)^{4}\) (c) \(\left(e^{3}\right)^{-2}\) (d) \(e^{0}\)

Problem 1

Find the derivative of the function. $$ f(x)=3 e $$

Problem 1

In Exercises \(1-8\), write the logarithmic equation as an exponential equation, or vice versa. $$ \ln 2=0.6931 $$

Problem 1

Exercises \(1-22\), find the derivative of the function. $$ y=\ln x^{2} $$

Problem 2

Use the properties of exponents to simplify the expression. (a) \(\frac{5^{3}}{5^{6}}\) (b) \(\left(\frac{1}{5}\right)^{-2}\) (c) \(\left(8^{1 / 2}\right)\left(2^{1 / 2}\right)\) (d) \(\left(32^{3 / 2}\right)\left(\frac{1}{2}\right)^{3 / 2}\)

Problem 2

Find the derivative of the function. $$ f(x)=-5 e $$

Problem 2

Find the derivative of the function. $$ f(x)=\ln 7 x $$

Problem 2

In Exercises , write the logarithmic equation as an exponential equation, or vice versa. $$ \ln 9=2.1972 $$

Problem 3

Use the properties of exponents to simplify the expression. (a) \(\frac{5^{3}}{25^{2}}\) (b) \(\left(9^{2 / 3}\right)(3)\left(3^{2 / 3}\right)\) (c) \(\left[\left(25^{1 / 2}\right)\left(5^{2}\right)\right]^{1 / 3}\) (d) \(\left(8^{2}\right)\left(4^{3}\right)\)

Problem 3

Find the derivative of the function. $$ y=e^{5 x} $$