Chapter 4

Solve for \(x\).\(5^{x}=125\)

Write the logarithm in terms of common logarithms.\(\log _{5} 8\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\((2.6)^{1.3}\)

Solve for \(x\).\(2^{x}=64\)

Write the logarithm in terms of common logarithms.\(\log _{7} 12\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\((1.07)^{50}\)

Solve for \(x\).\(7^{x}=\frac{1}{49}\)

Write the logarithm in terms of common logarithms.\(\ln 30\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\(100(1.03)^{-1.4}\)

Solve for \(x\).\(4^{x}=\frac{1}{256}\)

Write the logarithm in terms of common logarithms.\(\ln 20\)

Match the logarithmic equation with its exponential form. [The exponential forms are labeled (a), (b), (c), (d), (e), and (f).]\(\log _{4} \frac{1}{16}=-2 \quad\) (d) \(4^{-2}=\frac{1}{16}\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\(1500\left(2^{-5 / 2}\right)\)

Solve for \(x\).\(4^{2 x-1}=64\)

Write the logarithm in terms of common logarithms.\(\log _{3} n\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\(6^{-\sqrt{2}}\)

Solve for \(x\).\(3^{x-1}=27\)

Write the logarithm in terms of common logarithms.\(\log _{4} m\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\(1.3^{\sqrt{5}}\)

Solve for \(x\).\(\log _{4} x=3\)

Write the logarithm in terms of common logarithms.\(\log _{1 / 5} x\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$4^{4}=256\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\(e^{4}\)

Solve for \(x\).\(\log _{5} 5 x=2\)

Write the logarithm in terms of common logarithms.\(\log _{1 / 3} x\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$7^{3}=343\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\(e^{-5}\)

Solve for \(x\).\(\log _{10} x=-1\)

Write the logarithm in terms of common logarithms.\(\log _{x} \frac{3}{10}\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$81^{1 / 4}=3\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\(e^{2 / 3}\)

Solve for \(x\).\(\ln (2 x-1)=0\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$9^{3 / 2}=27\)

Use a calculator to evaluate the expression. Round your result to three decimal places.\(e^{-2.7}\)

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression.\(\ln e^{x^{2}}\)

Write the logarithm in terms of common logarithms.\(\log _{2.6} x\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$6^{-2}=\frac{1}{36}\)

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression.\(\ln e^{2 x-1}\)

Write the logarithm in terms of common logarithms.\(\log _{7.1} x\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$10^{-3}=0.001\)

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression.\(\log _{10} 10^{x^{2}}+1\)

Write the logarithm in terms of natural logarithms. \(\log _{5} 8\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$e^{1}=e\)

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression.\(\log _{10} 10^{2 x+3}\)

Write the logarithm in terms of natural logarithms.\(\log _{7} 12\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$e^{4}=54.5981 \ldots\)

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression.\(\log _{5} 5^{x^{3}}-7\)

Write the logarithm in terms of natural logarithms.\(\log _{10} 5\)

Use the definition of a logarithm to write the equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3$$e^{x}=4\)

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression.\(\log _{8} 8^{x^{5}}+1\)