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Chapter 12: Problem 24

Evaluate each expression without using a calculator. $$\log _{3} 27$$

Short Answer

Expert verified
The value of \(\log_{3} 27\) is 3.

Step by step solution

01

Identifying base and number

In the expression \(\log_{3} 27\), 3 is the base and 27 is the number. A logarithm answers the question: 'To what exponent should we raise the base to obtain the number?'.
02

Finding the exponent

\(\log_{3} 27\) asks: '3 to what power equals 27?'. Evaluate the exponent required. By knowledge of basic exponent rules, we find that \(3^{3} = 27\). So, the exponent required is 3.

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Most popular questions from this chapter

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. $$\log (x+3)+\log x=1$$

Solve: $$\frac{3}{x+1}-\frac{5}{x}=\frac{19}{x^{2}+x}$$

Describe the change-of-base property and give an example.

Solve each equation. $$3^{x+2} \cdot 3^{x}=81$$

Solve each equation in Exercises \(144-146 .\) Check each proposed solution by direct substitution or with a graphing utility. $$\ln (\ln x)=0$$
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