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Chapter 10: Q. 292 (page 1054)

In the following exercise, solve for x.

log5(4x鈭�2)=log510

Short Answer

Expert verified

The solution of the given expression isx=3

Step by step solution

01

Step 1. Given information.   

The given expression log5(4x鈭�2)=log510

02

Step 2. Use logarithmic properties    

Using one to one property, we get:

log5(4x鈭�2)=log5104x-2=104x=12

03

Step 3. Solve for x.

Solving the equation, we get:

4x=124x4=124dividingbothsidesby4x=3

04

Step 4. Check the value  

Substituting x=3in the given expression, we get:

log5(4x鈭�2)=log510log54路3-2=log510log510=log510

This is true.

Thus, x=3is the solution of the given function.

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