91Ó°ÊÓ

Solve for \(y\) in terms of \(x\) $$2 \log _{5} x-\log _{5} y=2$$

Perform the indicated operations. $$\text { Evaluate: (a) } \log _{b} b \quad \text { (b) } \log _{b} 1$$

Solve for \(y\) in terms of \(x\) $$\log _{8} x=2 \log _{8} y+4$$

Use a calculator to solve the given equations. Measured on the Richter scale, the magnitude of an earthquake of intensity \(I\) is defined as \(R=\log \left(I / I_{0}\right),\) where \(I_{0}\) is a minimum level for comparison. How many times \(I_{0}\) was the 1906 San Francisco earthquake whose magnitude was 8.3 on the Richter scale?

Perform the indicated operations. $$\text { If } f(x)=\log _{5} x, \text { find: }(a) f(\sqrt{5}) \quad \text { (b) } f(0)$$

\(\text {Solve the given problems.}\) $$\text { Explain why } \log _{10}(x+3) \text { is not equal to } \log _{10} x+\log _{10} 3$$

Perform the indicated operations. If \(f(x)=\log _{b} x\) and \(f(3)=2,\) find \(f(9)\)

\(\text {Solve the given problems.}\) Express as the logarithm of a single quantity: \(2 \log _{2}(2 x)-\log _{2} x^{2}\) For what values of \(x\) is the value of this expression valid? Explain.

Use a calculator to solve the given equations. Studies have shown that the concentration \(c\) (in \(\mathrm{mg} / \mathrm{cm}^{3}\) of blood) of aspirin in a typical person is related to the time \(t\) (in h) after the aspirin reaches maximum concentration by the equation \(\ln c=\ln 15-0.20 t .\) Solve for \(c\) as a function of \(t.\)

Perform the indicated operations. Find \(b\) such that the point (2,2) is on the graph of \(y=\log _{b} x\)