Chapter 10: Q. 462 (page 1068)

Solve for x:
$\log (x^{2} - 39) = 1$

Short Answer

Expert verified

The value of $x$ is $\pm 7$

Step by step solution

Step 1. Given

An expression is given as $\log (x^{2} - 39) = 1$

Step 2. Calculation

First convert it into exponential form,

$\log (x^{2} - 39) = 1 \to x^{2} - 39 = 10^{1}$

Now simplify it,

$x^{2} - 39 = 10 x^{2} = 49 x = \pm \sqrt{49} x = \pm 7$

Step 3. Verification

Put the values in the original equation,

$\begin{array}{r} \log (7^{2} - 39) = 1 \\ \log (49 - 39) = 1 \\ \log 10 = 1 \\ 1 = 1 \end{array}$

and

$\begin{array}{r} \log [(- 7)^{2} - 39] = 1 \\ \log (49 - 39) = 1 \\ \log 10 = 1 \\ 1 = 1 \end{array}$

In both cases LHS is equal to RHS.

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Solve for x:
$\log (x^{2} - 39) = 1$

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

Step 3. Verification

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Solve for x:logx2-39=1

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

Step 3. Verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Decision Maths

Mechanics Maths

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve for x:
$\log (x^{2} - 39) = 1$