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Chapter 10: Q. 197 (page 1034)

In the following exercises,solve each logarithmic equation.

log2(6x+2)=5.

Short Answer

Expert verified

The solution isx=5.

Step by step solution

01

Step 1.Given information

Consider the logarithmic equation log2(6x+2)=5

The logarithmic fromy=logax is equivalent to exponential formx=ay

02

Step 2.Solve the given logarithmic equation.

Comparing log2(6x+2)=5with the standard form y=logax,you have y=5,a=2,x=6x+2

Convert logarithmic equation in exponential equation as shown below

So,the equation 6x+2=32

Now solve the equation as

role="math" localid="1645010996064" 6x+2-2=32-26x=30[Substract2]x=306[divide]x=5

03

Step 3.Check

To check the solution,replace a by 5 in original equation

log2(6.5+2)=5[x=5]log2(30+2)=5log2(32)=525=3232=32[true]

Therefore,the solution isx=5

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