Chapter 5: Q 33. (page 298)

Find the exact value of the logarithm without using a calculator.
$\log_{\sqrt{2}} (4)$

Short Answer

Expert verified

The exact value of the logarithm is 4.

Step by step solution

Step 1. Given information

A logarithmic function is given as $\log_{\sqrt{2}} (4)$ .

Step 2. Formula Used

The logarithmic function $y = \log_{a} (x)$ can be changed into an exponential statement as $x = a^{y}$ .

Step 3. Finding Value of the logarithm

Consider $\log_{\sqrt{2}} (4) = x$

By changing rule of logarithm to exponential function,

${\sqrt{2}}^{x} = 4 {\sqrt{2}}^{x} = {\sqrt{2}}^{4} x = 4 \log_{\sqrt{2}} (4) = 4$

The required value is,

$\log_{\sqrt{2}} (4) = 4$

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Find the exact value of the logarithm without using a calculator.
$\log_{\sqrt{2}} (4)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula Used

Step 3. Finding Value of the logarithm

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Find the exact value of the logarithm without using a calculator.log24

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula Used

Step 3. Finding Value of the logarithm

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the exact value of the logarithm without using a calculator.
$\log_{\sqrt{2}} (4)$