91Ó°ÊÓ

Explain how you could use the following table of values for the function \(f(x)=10^{x}\) to find the given quantity. $$\begin{array}{cc} x & f(x)=10^{x} \\ 0.4771 & 3 \\ 0.5 & \sqrt{10} \\ 3 & 1000 \\ -0.3010 & 0.5 \\ \sqrt{10} & 1452 \end{array}$$ $$. \log 1000$$

Solve using any method, and eliminate extraneous solutions. $$e^{\log x}=e$$

Explain how you could use the following table of values for the function \(f(x)=10^{x}\) to find the given quantity. $$\begin{array}{cc} x & f(x)=10^{x} \\ 0.4771 & 3 \\ 0.5 & \sqrt{10} \\ 3 & 1000 \\ -0.3010 & 0.5 \\ \sqrt{10} & 1452 \end{array}$$ $$\log 3$$

Solve using any method, and eliminate extraneous solutions. $$\log _{5}|x-2|=2$$

Explain how you could use the following table of values for the function \(f(x)=10^{x}\) to find the given quantity. $$\begin{array}{cc} x & f(x)=10^{x} \\ 0.4771 & 3 \\ 0.5 & \sqrt{10} \\ 3 & 1000 \\ -0.3010 & 0.5 \\ \sqrt{10} & 1452 \end{array}$$ $$\log 0.5$$

Solve using any method, and eliminate extraneous solutions. $$\ln |2 x-3|=1$$

Explain how you could use the following table of values for the function \(f(x)=10^{x}\) to find the given quantity. $$\begin{array}{cc} x & f(x)=10^{x} \\ 0.4771 & 3 \\ 0.5 & \sqrt{10} \\ 3 & 1000 \\ -0.3010 & 0.5 \\ \sqrt{10} & 1452 \end{array}$$ $$\log \sqrt{10}$$

The graph of \(f(x)=a \log x\) passes through the point \((10,3) .\) Find \(a\) and thus the complete expression for \(f\) Check your answer by graphing \(f\).

The graph of \(f(x)=A \ln x+B\) passes through the points (1,2) and \((e, 4)\) (a) Find \(A\) and \(B\) using the given points. (b) Check your answer by graphing \(f\)

Sketch graphs of the two functions to show that \(\log _{1 / 2} x=-\log _{2} x .\) (The equality can be established algebraically by techniques in the following section.)