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Chapter 3: Problem 101

Determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. $$\log _{3} 7=\frac{1}{\log _{7} 3}$$

Short Answer

Expert verified
The equation is true, following the change of base formula of logarithm.

Step by step solution

01

Recall Logarithmic Properties

Start by recalling the change of base formula for logarithms: \( \log _{b} a=\frac{1}{\log _{a} b} \) .
02

Comparing the Formulas

Next, compare the given equation with the change of base formula. Since both of them are having the same pattern, it is apparent that the given equation is in the form of the change of base formula for logarithm.
03

Conclusion

Based on the comparison, it is concluded that the equation is indeed a true statement because it follows the change of base formula of logarithm with \( a=7, b=3 \) .

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Most popular questions from this chapter

Solve the equation \(x^{3}-9 x^{2}+26 x-24=0\) given that 4 is a zero of \(f(x)=x^{3}-9 x^{2}+26 x-24 .\) (Section 2.4 Example \(6)\)

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