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Magazine Problem 1
Without using a calculator or computer, give a rough estimate of \(2^{83}\).
Problem 1
The next two exercises emphasize that \(\log (x+y)\) does not equal \(\log x+\log y\). For \(x=7\) and \(y=13,\) evaluate: (a) \(\log (x+y)\) (b) \(\log x+\log y\)
Problem 1
The next two exercises emphasize that \(\ln (x+y)\) does not equal \(\ln x+\ln y\). For \(x=7\) and \(y=13,\) evaluate each of the following: (a) \(\ln (x+y)\) (b) \(\ln x+\ln y\)
Problem 1
Emphasize that \(\log \left(x^{y}\right)\) does not equal \((\log x)^{y}\) \(\quad\) For \(x=5\) and \(y=2,\) evaluate each of the following: (a) \(\log \left(x^{y}\right)\) (b) \((\log x)^{y}\)
Problem 1
Evaluate the indicated quantities assuming that \(f\) and \(g\) are the functions defined by $$ f(x)=2^{x} \quad \text { and } \quad g(x)=\frac{x+1}{x+2} . $$ $$ (f \circ g)(-1) $$
Problem 1
For Exercises 1-18, estimate the indicated value without using a calculator. \(\ln 1.003\)
Problem 1
How much would an initial amount of \(\$ 2000,\) compounded continuously at \(6 \%\) annual interest, become after 25 years?
Problem 2
Emphasize that \(\log \left(x^{y}\right)\) does not equal \((\log x)^{y}\) For \(x=2\) and \(y=3,\) evaluate each of the following: (a) \(\log \left(x^{y}\right)\) (b) \((\log x)^{y}\)
Problem 2
Estimate the indicated value without using a calculator. \(\ln 1.0007\)
Problem 2
The next two exercises emphasize that \(\log (x+y)\) does not equal \(\log x+\log y\). For \(x=0.4\) and \(y=3.5,\) evaluate: (a) \(\log (x+y)\) (b) \(\log x+\log y\)
