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Chapter 10: Q 291E. (page 1005)

In the following exercise, solve for x.

3log6x=log664

Short Answer

Expert verified

The solution of the given expression isx=4

Step by step solution

01

Step 1. Given information.  

The given expression3log6x=log664

02

Step 2. Use logarithmic properties   

Using power property, we get:

3log6x=log664log6x3=log664

Using one to one property, we get:

x3=64

03

Step 3. Solve for x.    

Solving the equation, we get:

x3=64x=643cubingrootbothsidesx=4

04

Step 4. Check the value 

Substituting x=4in the given expression, we get:

3log6x=log6643log64=log664log643=log664log664=log664

This is true

Thus x=4is the solution of the given function.

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