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Chapter 10: Q. 204 (page 1035)

In the following exercises, solve each logarithmic equation.

logx2=2

Short Answer

Expert verified

The solutions are x=10and

x=-10.

Step by step solution

01

Step 1. Rewrite in exponential form and simplify

Consider the logarithmic equation logx2=2.

Its equivalent exponential form is given as

102=x2

It can be simplified to

100=x2

02

Step 2. Solve the quadratic equation for x

Set the left hand side equal to zero, by subtracting 100from both sides.

role="math" localid="1644948956203" 100-100=x2-1000=x2-100

Factor the right hand side and solve the equation.

0=x2-1000=x2-1020=(x-10)(x+10)

So the solutions are

x-10=0x=10or

x+10=0x=-10

03

Step 3. Check for the first solution

Substitute 10for xin the original equation, we get

role="math" localid="1644949080556" logx2=2log102=2log100=22=2

So we get a true statement, thus the found solution is correct.

04

Step 4. Check for the second solution

Substitute -10for xin the original equation, we get

logx2=2log(-10)2=2log100=22=2

So we get a true statement, thus the found solution is correct.

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