Chapter 10: Q. 288 (page 1054)

In the following exercise, solve for x.
$\log_{4} 64 = 2 \log_{4} x$

Short Answer

Expert verified

The solution of the given function is $x = 8$

Step by step solution

Step 1. Given information

The given information is $\log_{4} 64 = 2 \log_{4} x$

Step 2. Use logarithmic properties

Using power property, we get:

$\log_{4} 64 = 2 {\log_{4}}^{x} \log_{4} 64 = {\log_{4}}^{x^{2}}$

Using one to one property, we get:

$\log_{4} 64 = \log_{4} x^{2} 64 = x^{2}$

Step 3. Solve for x.

Solving the equation, we get:

$x^{2} = 64 x = \pm \sqrt{64} [r o o t i n g b o o t h s i d e s] x = \pm 8$

We can eliminate $x = - 8$ because the logarithmic function doesn't take negative values.

Step 4. Check the values

Substituting $x = 8$ in the given expression, we get:

$\log_{4} 64 = 2 \log_{4} x \log_{4} 64 = 2 \log_{4} 8 \log_{4} 64 = \log_{4} 64$

This is true.

Thus $x = 8$ is the solution of the given function.

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In the following exercise, solve for x.
$\log_{4} 64 = 2 \log_{4} x$

Short Answer

Step by step solution

Step 1. 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.log464=2log4x

Short Answer

Step by step solution

Step 1. 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

Calculus

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Statistics

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Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, solve for x.
$\log_{4} 64 = 2 \log_{4} x$