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Chapter 3: Problem 67
Condense the expression to the logarithm of a single quantity. $$\ln 2+\ln x$$
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The IQ scores for a sample of a class of returning adult students at a small northeastern college roughly follow the normal distribution \(y=0.0266 e^{-(x-100)^{2} / 450}, 70 \leq x \leq 115,\) where \(x\) is the IQ score. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average IQ score of an adult student.
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{2}(2 x-3)=\log _{2}(x+4)$$
Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$\ln (x+1)=2-\ln x$$
Find the exponential model \(y=a e^{b x}\) that fits the points shown in the graph or table. $$ \begin{array}{|l|l|l|} \hline x & 0 & 3 \\ \hline y & 1 & \frac{1}{4} \\ \hline \end{array} $$
Determine whether the statement is true or false. Justify your answer. The domain of a logistic growth function cannot be the set of real numbers.
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