Chapter 10: Q. 289 (page 1054)

In the following exercise, solve for x.
$\log 49 = 2 \log x$

Short Answer

Expert verified

The solution of the given expression is $x = 7$

Step by step solution

. Given information.

The given expression is $\log 49 = 2 \log x$ $\log 49 = 2 \log x$

Step 2. Use logarithmic properties

Using power property, we get:

$\log 49 = 2 \log x \log 49 = \log x^{2}$

Using one to one property, we get:

$\log 49 = \log x^{2} 49 = x^{2} x^{2} = 49$

Step 3. Solve for x.

Solving the equation, we get:

$x^{2} = 49 x = \pm \sqrt{49} [r o o t i n g b o t h s i d e s] x = \pm 7$

We can eliminate $x = - 7$ because the logarithmic function doesn't take negative values.

Step 4. Check the values

Substituting $x = 7$ in the given expression, we get:

$\log 49 = 2 \log x \log 49 = 2 \log 7 \log 49 = \log 7^{2} \log 49 = \log 49$

This is True.

Thus $x = 7$ is the solution of the given function.

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In the following exercise, solve for x.
$\log 49 = 2 \log x$

Short Answer

Step by step solution

. Given information.

Step 2. Use logarithmic properties

Step 3. Solve for x.

Step 4. Check the values

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In the following exercise, solve for x.log49=2logx

Short Answer

Step by step solution

. Given information.

Step 2. Use logarithmic properties

Step 3. Solve for x.

Step 4. Check the values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercise, solve for x.
$\log 49 = 2 \log x$