Chapter 10: Q. 258 (page 1045)

In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible.
$\log_{2} \frac{\sqrt{2 x + y^{2}}}{z^{2}}$

Short Answer

Expert verified

The simplified expression is,

$\frac{1}{2} \log_{2} (2 x + y^{2}) - 2 \log_{2} z$

Step by step solution

Step 1. Given and explanation

We are given an expression,

$\log_{2} \frac{\sqrt{2 x + y^{2}}}{z^{2}}$

Use the properties of logarithms to simplify the given expression.

Step 2. Simplifying the expression

Using quotient property of logarithm , we get

$\log_{2} \frac{\sqrt{2 x + y^{2}}}{z^{2}} = \log_{2} \sqrt{2 x + y^{2}} - \log_{2} z^{2} \log_{2} \frac{\sqrt{2 x + y^{2}}}{z^{2}} = \log_{2} {(2 x + y^{2})}^{\frac{1}{2}} - \log_{2} z^{2}$

Now, using power property of logarithm , we get

$\log_{2} \frac{\sqrt{2 x + y^{2}}}{z^{2}} = \frac{1}{2} \log_{2} (2 x + y^{2}) - 2 \log_{2} z$

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In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible.
$\log_{2} \frac{\sqrt{2 x + y^{2}}}{z^{2}}$

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Simplifying the expression

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In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible.log22x+y2z2

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Simplifying the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Probability and Statistics

Pure Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible.
$\log_{2} \frac{\sqrt{2 x + y^{2}}}{z^{2}}$