91Ó°ÊÓ

Solve each logarithmic equation. Express irrational solutions in exact form. $$ \log (2 x)-\log (x-3)=1 $$

For the given functions fand \(g\), find: (a) \(f^{\circ} g\) (b) \(g^{\circ} f\) (c) \(f \circ f\) (d) \(g^{\circ}\) g State the domain of each composite function. \(f(x)=-x ; \quad g(x)=2 x-4\)

Change each logarithmic statement to an equivalent statement involving an exponent. $$ \ln 4=x $$

Solve each logarithmic equation. Express irrational solutions in exact form. $$ \log _{2}(x+7)+\log _{2}(x+8)=1 $$

Use properties of logarithms to find the exact value of each expression. Do not use a calculator. \(4^{\log _{4} 6-\log _{4} 5}\)

Approximate each number using a calculator. Express your answer rounded to three decimal places $$ e^{1.2} $$

The logistic model $$P(n)=\frac{113.3198}{1+0.115 e^{0.0912 n}}$$ models the probability that, in a room of \(n\) people, no two people share the same birthday. (a) Use a graphing utility to graph \(P=P(n)\). (b) In a room of \(n=15\) people, what is the probability that no two share the same birthday? (c) How many people must be in a room before the probability that no two people share the same birthday falls below \(10 \% ?\) (d) What happens to the probability as \(n\) increases? Explain what this result means.

For the given functions fand \(g\), find: (a) \(f^{\circ} g\) (b) \(g^{\circ} f\) (c) \(f \circ f\) (d) \(g^{\circ}\) g State the domain of each composite function. \(f(x)=3 x-1 ; \quad g(x)=x^{2}\)

Find the effective rate of interest. For \(6 \%\) compounded continuously

Approximate each number using a calculator. Express your answer rounded to three decimal places $$ e^{-1.3} $$