Chapter 10: Q 291E. (page 1005)

In the following exercise, solve for x.
$3 \log_{6} x = \log_{6} 64$

Short Answer

Expert verified

The solution of the given expression is $x = 4$

Step by step solution

Step 1. Given information.

The given expression $3 \log_{6} x = \log_{6} 64$

Step 2. Use logarithmic properties

Using power property, we get:

$3 \log_{6} x = \log_{6} 64 \log_{6} x^{3} = \log_{6} 64$

Using one to one property, we get:

$x^{3} = 64$

Step 3. Solve for x.

Solving the equation, we get:

$x^{3} = 64 x = \sqrt[3]{64} [c u b i n g r o o t b o t h s i d e s] x = 4$

Step 4. Check the value

Substituting $x = 4$ in the given expression, we get:

$3 \log_{6} x = \log_{6} 64 3 \log_{6} 4 = \log_{6} 64 \log_{6} 4^{3} = \log_{6} 64 \log_{6} 64 = \log_{6} 64$

This is true

Thus $x = 4$ is the solution of the given function.

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In the following exercise, solve for x.
$3 \log_{6} x = \log_{6} 64$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use logarithmic properties

Step 3. Solve for x.

Step 4. Check the value

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In the following exercise, solve for x.3log6x=log664

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use logarithmic properties

Step 3. Solve for x.

Step 4. Check the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Probability and Statistics

Mechanics Maths

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, solve for x.
$3 \log_{6} x = \log_{6} 64$