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Chapter 10: Q. 195 (page 1034)

In the following exercises,solve each logarithmic equation

lnx=4.

Short Answer

Expert verified

The solution isx=e4.

Step by step solution

01

Step 1.Given information

Consider the logarithmic equation lnx=4.

The logarithmic fromy=lnx is equivalent to exponential formx=ey.

02

Step 2.Solve the given logarithmic equation

Comparing lnx=4with the standard form y=lnx ,you have y=4

Convert logarithmic equation in exponential equation as shown below

x=eyx=e4

So,the solution isx=e4

03

Step 3.Check

To check the solution,replace a by e4in original equation

lnx=4lne4=4[x=e4]4lne=44=4[true]

Therefore, the solution isx=e4

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