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Magazine Problem 51
Find the smallest integer \(M\) such that \(5^{1 / M}<1.01\).
Problem 51
For Exercises \(37-54\), find a formula for the inverse function \(f^{-1}\) of the indicated function \(f .\) $$ \begin{array}{l} f(x)= \\ 5+3 \log _{6}(2 x+1) \end{array} $$
Problem 52
For Exercises \(37-54\), find a formula for the inverse function \(f^{-1}\) of the indicated function \(f .\) $$ \begin{array}{l} f(x)= \\ 8+9 \log _{2}(4 x-7) \end{array} $$
Problem 52
Evaluate the indicated quantities assuming that \(f\) and \(g\) are the functions defined by \(f(x)=2^{x} \quad\) and \(\quad g(x)=\frac{x+1}{x+2}\). $$ (g \circ f)(0) $$
Problem 53
Suppose \(\log _{8}\left(\log _{7} m\right)=5 .\) How many digits does \(m\) have?
Problem 53
Evaluate the indicated quantities assuming that \(f\) and \(g\) are the functions defined by \(f(x)=2^{x} \quad\) and \(\quad g(x)=\frac{x+1}{x+2}\). $$ (f \circ g)(0) $$
Problem 54
Suppose \(\log _{5}\left(\log _{9} m\right)=6 .\) How many digits does \(m\) have?
Problem 54
Evaluate the indicated quantities assuming that \(f\) and \(g\) are the functions defined by \(f(x)=2^{x} \quad\) and \(\quad g(x)=\frac{x+1}{x+2}\). $$ (g \circ f)\left(\frac{3}{2}\right) $$
Problem 55
For Exercises \(55-58,\) find a formula for \((f \circ g)(x)\) assuming that \(f\) and \(g\) are the indicated functions. $$ f(x)=\log _{6} x \text { and } g(x)=6^{3 x} $$
Problem 55
Evaluate the indicated quantities assuming that \(f\) and \(g\) are the functions defined by \(f(x)=2^{x} \quad\) and \(\quad g(x)=\frac{x+1}{x+2}\). $$ (f \circ f)\left(\frac{1}{2}\right) $$
