Chapter 10: Q. 410 (page 1064)

In the following exercises, solve each logarithmic equation.
$\log (x^{2} - 21) = 2$ .

Short Answer

Expert verified

The solution is $x = 11, - 11$ .

Step by step solution

Step 1. Given and explanation.

We have $\log (x^{2} - 21) = 2$ .

We know that if there is an expression as $\log_{e} (x) = y$ , it means thatif we need to convert the logarithmic expression into exponential form.

Then simplifying the equation will give us the answer.

Step 2. Converting into exponential form.

We have $\log (x^{2} - 21) = 2$ .

This can also be written as $\log_{10} (x^{2} - 21) = 2$

Converting into exponential forms gives us,
$x^{2} - 21 = 10^{2}$

Step 3. Solving for x.

We have $x^{2} - 21 = 10^{2}$ .

Simplifying it gives us,

$x^{2} - 21 = 100 x^{2} = 100 + 21 x^{2} = 121 x = \pm 11$

Thus we get the solution as $x = \pm 11$ .

Step 4. Checking the solution.

We have $x = \pm 11$ .

Substituting the values give us,

When $x = 11$
$\log ({(11)}^{2} - 21) = 2 \log (121 - 21) = 2 \log (100) = 2 {(10)}^{2} = 2 2 = 2$
Hence verified.
When $x = - 11$
$\log ({(- 11)}^{2} - 21) = 2 \log (121 - 21) = 2 \log (100) = 2 {(10)}^{2} = 2 2 = 2$
Hence verified.

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In the following exercises, solve each logarithmic equation.
$\log (x^{2} - 21) = 2$ .

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Converting into exponential form.

Step 3. Solving for x.

Step 4. Checking the solution.

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In the following exercises, solve each logarithmic equation.log(x2-21)=2.

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Converting into exponential form.

Step 3. Solving for x.

Step 4. Checking the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each logarithmic equation.
$\log (x^{2} - 21) = 2$ .