Chapter 10: Q. 285 (page 1046)

Write the Power Property in your own words. Does it apply to each of the following? $\log_{a} x^{p}, (\log_{a} x^{r})$ , why or why not?

Short Answer

Expert verified

The power property of logarithm is used to write the log of a number raised to a power as the product of the power times the log of the number.

$\log_{a} M^{n} = n \log_{a} M$

The Power Property of logarithm is only applicable to $\log_{a} x^{p}$ and not to ${(\log_{a} x)}^{r}$ as te power is raised for both the exponent and logarithm

Step by step solution

Step 1. To explain

To explain about the power property.

$\log_{a} x^{p}, (\log_{a} x^{r})$

To find if the power property applies to the above equation.

Step 2. Power Property of logarithm

The power property of logarithm is used to write the log of a number raised to a power as the product of the power times the log of the number.

$\log_{a} M^{n} = n \log_{a} M$

Step 3. Applying to logaxp,(logax)r

Consider $\log_{a} x^{p}$

By Power Property of logarithm, the log of a number raised to a power as the product of the power times the log of the number. So,

$\log_{a} x^{p} = p \log_{a} x$

But in ${(\log_{a} x)}^{r}$ , the power is raised to both the power and logarrithm, so the power property is not applicabel here.

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Write the Power Property in your own words. Does it apply to each of the following? $\log_{a} x^{p}, (\log_{a} x^{r})$ , why or why not?

Short Answer

Step by step solution

Step 1. To explain

Step 2. Power Property of logarithm

Step 3. Applying to logaxp,(logax)r

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Write the Power Property in your own words. Does it apply to each of the following? logaxp,(logaxr), why or why not?

Short Answer

Step by step solution

Step 1. To explain

Step 2. Power Property of logarithm

Step 3. Applying to logaxp,(logax)r

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

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Pure Maths

Study anywhere. Anytime. Across all devices.

Write the Power Property in your own words. Does it apply to each of the following? $\log_{a} x^{p}, (\log_{a} x^{r})$ , why or why not?