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Magazine 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) \(\log x+\log y\)
Problem 2
The next two exercises emphasize that \(\ln (x+y)\) does not equal \(\ln x+\ln y\). For \(x=0.4\) and \(y=3.5\), evaluate each of the following: (a) \(\ln (x+y)\) (b) \(\ln x+\ln y\)
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 3
The next two exercises emphasize that \(\ln (x y)\) does not equal \((\ln x)(\ln y)\). For \(x=3\) and \(y=8\), evaluate each of the following: (a) \(\ln (x y)\) (b) \((\ln x)(\ln y)\)
Problem 3
The next two exercises emphasize that \(\log (x+y)\) does not equal \(\log x+\log y\). For \(x=3\) and \(y=8,\) evaluate: (a) \(\log (x y)\) (b) \((\log x)(\log y)\)
Problem 3
Suppose \(t\) is such that \(\log _{2} t=17.67 .\) Evaluate \(\log _{2}\left(t^{100}\right)\)
Problem 3
How much would you need to deposit in a bank account paying \(4 \%\) annual interest compounded continuously so that at the end of 10 years you would have \(\$ 10,000 ?\)
Problem 3
Without using a calculator or computer, determine which of the two numbers \(2^{125}\) and \(32 \cdot 10^{36}\) is larger.
Problem 3
Evaluate the indicated quantities assuming that \(f\) and \(g\) are the functions defined by $$ f(x)=2^{x} \quad \text { and } \quad g(x)=\frac{x+1}{x+2} . $$ $$ (f \circ g)(0) $$
Problem 4
The next two exercises emphasize that \(\ln (x y)\) does not equal \((\ln x)(\ln y)\). For \(x=1.1\) and \(y=5\), evaluate each of the following: (a) \(\ln (x y)\) (b) \((\ln x)(\ln y)\)
