Chapter 4

Evaluate each expression to four decimal places using a calculator. $$4^{1.6}$$

Use \(f(t)=10 e^{-t}\). For what value of \(t\) will \(f(t)=2 ?\)

Solve the exponential equation. Round to three decimal places, when needed. $$6^{x}=\frac{1}{216}$$

In Exercises \(7-14,\) use \(\log 2 \approx 0.3010, \log 5 \approx 0.6990,\) and \(\log 7 \approx 0.8451\) to evaluate each logarithm without using a calculator. Then check your answer using a calculator. $$\log \frac{5}{7}$$

Write 1,360,000,000,000 in scientific notation.

Verify that the given functions are inverses of each other. $$f(x)=x+7 ; g(x)=x-7$$

Evaluate each expression to four decimal places using a calculator. $$6^{2.5}$$

Solve the exponential equation. Round to three decimal places, when needed. $$4 e^{x}=36$$

use \(f(t)=10 e^{-t}\) Evaluate \(f(1)\)

In Exercises \(7-14,\) use \(\log 2 \approx 0.3010, \log 5 \approx 0.6990,\) and \(\log 7 \approx 0.8451\) to evaluate each logarithm without using a calculator. Then check your answer using a calculator. $$\log \sqrt{2}$$

Verify that the given functions are inverses of each other. $$f(x)=6 x ; g(x)=\frac{1}{6} x$$

Evaluate each expression to four decimal places using a calculator. $$3^{\sqrt{2}}$$

Use \(f(t)=4 e^{t}\) Evaluate \(f(3)\)

Solve the exponential equation. Round to three decimal places, when needed. $$.5 e^{x}=60$$

In Exercises \(7-14,\) use \(\log 2 \approx 0.3010, \log 5 \approx 0.6990,\) and \(\log 7 \approx 0.8451\) to evaluate each logarithm without using a calculator. Then check your answer using a calculator. $$\log \sqrt{5}$$

Verify that the given functions are inverses of each other. $$f(x)=-8 x ; g(x)=-\frac{1}{8} x$$

In Exercises \(11-14,\) use \(f(t)=4 e^{t}\) For what value of \(t\) will \(f(t)=8 ?\)

Solve the exponential equation. Round to three decimal places, when needed. $$2^{x}=5$$

In Exercises \(7-14,\) use \(\log 2 \approx 0.3010, \log 5 \approx 0.6990,\) and \(\log 7 \approx 0.8451\) to evaluate each logarithm without using a calculator. Then check your answer using a calculator. $$\log 125$$

Verify that the given functions are inverses of each other. $$f(x)=-3 x+8 ; g(x)=-\frac{1}{3} x+\frac{8}{3}$$

Evaluate each expression to four decimal places using a calculator. $$e^{3}$$

Solve the exponential equation. Round to three decimal places, when needed. $$3^{x}=7$$

Verify that the given functions are inverses of each other. $$f(x)=\frac{1}{2} x+1 ; g(x)=2 x-2$$

Evaluate each expression to four decimal places using a calculator. $$e^{6}$$

Use \(f(x)=\frac{10}{1+2 e^{-0.3 x}}\) Evaluate \(f(0)\).

Solve the exponential equation. Round to three decimal places, when needed. $$3\left(1.3^{x}\right)=5$$

In Exercises \(15-20,\) use the properties of logarithms to simplify each expression by eliminating all exponents and radicals. Assume that \(x, y > 0\). $$\log \left(x y^{3}\right)$$

Evaluate each expression without using a calculator. $$\log 10,000$$

Verify that the given functions are inverses of each other. $$f(x)=x^{3}+2 ; g(x)=\sqrt[3]{x-2}$$

Evaluate each expression to four decimal places using a calculator. $$e^{-2.5}$$

Use \(f(x)=\frac{10}{1+2 e^{-0.3 x}}\) Evaluate \(f(1)\).

Solve the exponential equation. Round to three decimal places, when needed. $$6\left(0.9^{x}\right)=7$$

In Exercises \(15-20,\) use the properties of logarithms to simplify each expression by eliminating all exponents and radicals. Assume that \(x, y > 0\). $$\log \left(x^{3} y^{2}\right)$$

Evaluate each expression without using a calculator. $$\log 0.001$$

Verify that the given functions are inverses of each other. $$f(x)=x^{3}-4 ; g(x)=\sqrt[3]{x+4}$$

Evaluate each expression to four decimal places using a calculator. $$e^{-3.2}$$

Use \(f(x)=\frac{10}{1+2 e^{-0.3 x}}\) Evaluate \(f(10)\).

Solve the exponential equation. Round to three decimal places, when needed. $$10^{x}=2^{-x+4}$$

In Exercises \(15-20,\) use the properties of logarithms to simplify each expression by eliminating all exponents and radicals. Assume that \(x, y > 0\). $$\log \sqrt[3]{x} \sqrt[4]{y}$$

Evaluate each expression without using a calculator. $$\log \sqrt[3]{10}$$

Verify that the given functions are inverses of each other. $$f(x)=x^{2}+3, x \geq 0 ; g(x)=\sqrt{x-3}$$

Sketch the graph of each function. $$f(x)=4^{x}$$

Use \(f(x)=\frac{10}{1+2 e^{-0.3 x}}\) Evaluate \(f(12)\).

Solve the exponential equation. Round to three decimal places, when needed. $$3^{-x}=10^{-4 x+1}$$

In Exercises \(15-20,\) use the properties of logarithms to simplify each expression by eliminating all exponents and radicals. Assume that \(x, y > 0\). $$\log \sqrt[5]{x^{2}} \sqrt{y^{5}}$$

Evaluate each expression without using a calculator. $$\log \sqrt{10}$$

Verify that the given functions are inverses of each other. $$f(x)=x^{2}-7, x \leq 0 ; g(x)=-\sqrt{x+7}$$

Sketch the graph of each function. $$f(x)=5^{x}$$

Use \(f(x)=3 \ln x-4\). Evaluate \(f(e)\).

Solve the exponential equation. Round to three decimal places, when needed. $$3^{-2 x-1}=2^{x}$$