Chapter 5: Q 36. (page 298)

Find the exact value of the logarithm without using a calculator.
$\ln (e^{3})$

Short Answer

Expert verified

The exact value of the logarithm is 3.

Step by step solution

Step 1. Given information

A logarithmic function is given as $\ln (e^{3})$ .

Step 2. Formula Used

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

Step 3. Finding Value of the logarithm

Consider $\ln (e^{3}) = x$

By changing rule of logarithm to exponential function,

$e^{x} = e^{3} e^{x} = e^{3} x = 3 \ln (e^{3}) = 3$

The required value is,

$\ln (e^{3}) = 3$

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Find the exact value of the logarithm without using a calculator.
$\ln (e^{3})$

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.lne3

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

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Find the exact value of the logarithm without using a calculator.
$\ln (e^{3})$