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Chapter 4: Problem 106

Describe the quotient rule for logarithms and give an example.

Short Answer

Expert verified
The quotient rule for logarithms states that the logarithm of a quotient equals the logarithm of the numerator minus the logarithm of the denominator. An example is \(\log_{2}{\frac{8}{4}}\), which equals \( \log_{2}{8} - \log_{2}{4} = 1\).

Step by step solution

01

Describe the Quotient Rule for Logarithms

The quotient rule for logarithms states that the logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Written in mathematical terms: \(\log_{b}{\frac{m}{n}} = \log_{b}{m} - \log_{b}{n}\) . Here, 'b' is the base of the logarithm, while 'm' and 'n' represent the numerator and the denominator, respectively.
02

Giving an example

Here's an example illustrating the quotient rule for logarithms: Consider \(\log_{2}{\frac{8}{4}}\). According to the quotient rule, this can be rewritten as \( \log_{2}{8} - \log_{2}{4}\) .
03

Calculating the Logarithm

\(\log_{2}{8} - \log_{2}{4} = 3 - 2 = 1 \). So, \(\log_{2}{\frac{8}{4}} = 1\).

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Most popular questions from this chapter

Find the domain of each logarithmic function. $$ f(x)=\log (7-x) $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{\log _{2} 8}{\log _{2} 4}=\frac{8}{4}$$

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. $$ \log (x-15)+\log x=2 $$

Evaluate or simplify each expression without using a calculator. $$ e^{\ln 300} $$

The figure shows the graph of \(f(x)=\ln x\). Use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. (GRAPH CANNOT COPY). $$ h(x)=-\ln x $$
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