Chapter 10: Q. 402 (page 1064)

In the following exercises, find the exact value of each logarithm without using a calculator.
$\log_{3} (\frac{1}{9})$

Short Answer

Expert verified

The value is $- 2$ .

Step by step solution

Step 1. Form a logarithmic equation and write its equivalent exponential form

Consider the expression $\log_{3} (\frac{1}{9})$ .

Setting the expression equal to $x$ we get,

$\log_{3} (\frac{1}{9}) = x$

And its equivalent exponential form is given as $3^{x} = \frac{1}{9}$ .

Step 2. Compare the exponents

The number $\frac{1}{9}$ can be equivalently written as $3^{- 2}$ . So we get

$3^{x} = \frac{1}{9} 3^{x} = 3^{- 2}$

Now, as the base is the same, so on comparing the exponents we get

$x = - 2$

Thus the value of $\log_{3} (\frac{1}{9})$ is $- 2$ .

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In the following exercises, find the exact value of each logarithm without using a calculator.
$\log_{3} (\frac{1}{9})$

Short Answer

Step by step solution

Step 1. Form a logarithmic equation and write its equivalent exponential form

Step 2. Compare the exponents

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In the following exercises, find the exact value of each logarithm without using a calculator.log319

Short Answer

Step by step solution

Step 1. Form a logarithmic equation and write its equivalent exponential form

Step 2. Compare the exponents

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, find the exact value of each logarithm without using a calculator.
$\log_{3} (\frac{1}{9})$