91Ó°ÊÓ

Use a calculator to evaluate the expression, correct to four decimal places. (a) \(\ln 5\) (b) \(\ln 25.3\) (c) \(\ln (1+\sqrt{3})\)

Use a calculator to evaluate the expression, correct to four decimal places. (a) \(\ln 27\) (b) \(\ln 7.39\) (c) \(\ln 54.6\)

Use the Laws of Logarithms to expand the expression. $$\log \sqrt{x \sqrt{y \sqrt{z}}}$$

These exercises deal with logarithmic scales. The Northridge, California, earthquake of 1994 had a magnitude of 6.8 on the Richter scale. A year later, a 7.2-magnitude earthquake struck Kobe, Japan. How many times more intense was the Kobe earthquake than the Northridge earthquake?

Solve the logarithmic equation for \(x\). $$\ln (2+x)=1$$

Solve the logarithmic equation for \(x\). $$\log x=-2$$

These exercises deal with logarithmic scales. The 1985 Mexico City earthquake had a magnitude of 8.1 on the Richter scale. The 1976 earthquake in Tangshan, China, was 1.26 times as intense. What was the magnitude of the Tangshan earthquake?

Use the Laws of Logarithms to expand the expression. \ln \left(\frac{x^{3} \sqrt{x-1}}{3 x+4}\right)

These exercises deal with logarithmic scales. The intensity of the sound of traffic at a busy intersection was measured at \(2.0 \times 10^{-5} \mathrm{W} / \mathrm{m}^{2}\) Find the intensity level in decibels.

Use the Laws of Logarithms to expand the expression. $$\log \left(\frac{10^{x}}{x\left(x^{2}+1\right)\left(x^{4}+2\right)}\right)$$