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Chapter 12: Problem 2
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{8}(13 \cdot 7)$$
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Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$3^{x}=2 x+3$$
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can use any positive number other than 1 in the changeof-base property, but the only practical bases are 10 and \(e\) because my calculator gives logarithms for these two bases.
I can solve \(4^{x}=15\) by writing the equation in logarithmic form.
$$\text { Divide and simplify: } \frac{\sqrt[3]{40 x^{2} y^{6}}}{\sqrt[3]{5 x y}}$$
Complete the table for a savings account subject to n compounding periods per year \(\left[A=P\left(1+\frac{r}{n}\right)^{n t}\right]\) Round answers to one decimal place. $$\begin{array}{l|c|l|l|l} \hline \begin{array}{l} \text { Amount } \\ \text { Invested } \end{array} & \begin{array}{l} \text { Number of } \\ \text { Compounding } \\ \text { Periods } \end{array} & \begin{array}{l} \text { Annual Interest } \\ \text { Rate } \end{array} & \begin{array}{l} \text { Accumulated } \\ \text { Amount } \end{array} & \begin{array}{l} \text { Time } t \\ \text { in Years } \end{array} \\ \hline \$ 1000 & 360 & & \$ 1400 & 2 \\ \hline \end{array}$$
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