91Ó°ÊÓ

If \(f(x)=4^{x},\) find each value indicated. In Exercise 50, use a calculator, and give the answer to the nearest hundredth. \(f\left(-\frac{1}{2}\right)\)

Use the change-of-base rule (with either common or natural logarithms) to find each logarithm to four decimal places. \(\log _{7} 4\)

Explain why 1 is not allowed as a base for a logarithmic function.

Solve each problem. See Example 6. According to selected figures from the last two decades of the 20 th century, the number of trillion cubic feet of dry natural gas consumed worldwide can be approximated by the function defined by $$ f(x)=51.47+6.044 \log _{2} x $$ where \(x=1\) corresponds to \(1980, x=2\) to \(1981,\) and so on. (Source: Energy Information Administration.) Use the function to approximate, to the nearest hundredth, consumption in each year. (a) 1980 (b) 1987 (c) 1995

Solve equation. \(\log _{1 / 2} 8=x\)

Simplify each expression. Write answers using only positive exponents. See Sections 4.1 and 4.2. $$ \frac{7^{8}}{7^{-4}} $$