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Chapter 10: Q. 201 (page 1034)

In the following exercises, solve each logarithmic equation.

log43x-2=2

Short Answer

Expert verified

The solution is x=6.

Step by step solution

01

Step 1. Rewrite in exponential form and simplify. 

Consider the logarithmic equation log43x-2=2.

Its equivalent exponential form is given as

42=3x-2

On simplifying we get,

16=3x-2

02

Step 2. Solve for x

Add 2to both sides of the equation.

16+2=3x-2+218=3x

Now divide both sides by 3.

183=3x36=x

03

Step 3. Check the solution 

Substitute 6for xin the original equation, we get

log43脳6-2=2log418-2=2log416=242=1616=16

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

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