91Ó°ÊÓ

Find the inverse of \(f(x)=2^{x}, x \geq 0\), together with its domain, and graph both functions in the same coordinate system.

Use the indicated base to logarithmically transform each exponential relationship so that a linear relationship results. Then use the indicated base to graph each relationship in a coordinate system whose axes are accordingly transformed so that a straight line results. $$ y=2^{x} ; \text { base } 2 $$

Find the inverse of \(f(x)=\left(\frac{1}{2}\right)^{x}, x \geq 0\), together with its domain, and graph both functions in the same coordinate system.

Simplify the following expressions: (a) \(-\ln \frac{1}{5}\) (b) \(\ln \frac{x^{2}-y^{2}}{-\sqrt{x}}\) (c) \(\log _{3} 3^{2 x+1}\)

Use the indicated base to logarithmically transform each exponential relationship so that a linear relationship results. Then use the indicated base to graph each relationship in a coordinate system whose axes are accordingly transformed so that a straight line results. $$ y=3^{x} ; \text { base } 3 $$

Solve for \(x\). (a) \(e^{3 x-1}=2\) (b) \(e^{-2 x}=10\) (c) \(e^{x^{2}-1}=10\)

Use the indicated base to logarithmically transform each exponential relationship so that a linear relationship results. Then use the indicated base to graph each relationship in a coordinate system whose axes are accordingly transformed so that a straight line results. $$ y=2^{-x} ; \text { base } 2 $$

Simplify the following expressions: (a) \(2^{5 \log _{2} x}\) (b) \(3^{4 \log _{3} x}\) (c) \(5^{5 \log _{1 / 5} x}\) (d) \(4^{-2 \log _{2} x}\) (e) \(2^{3 \log _{1 / 2} x}\) (f) \(4^{-\log _{1 / 2} x}\)

Use the indicated base to logarithmically transform each exponential relationship so that a linear relationship results. Then use the indicated base to graph each relationship in a coordinate system whose axes are accordingly transformed so that a straight line results. $$ y=3^{-x} ; \text { base } 3 $$

Solve for \(x\). (a) \(3^{x}=81\) (b) \(9^{2 x+1}=27\) (c) \(10^{5 x}=1000\)