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Chapter 10: Q. 290 (page 1054)

In the following exercise, solve for x.

3log3x=log327

Short Answer

Expert verified

The solution of the given expression isx=3

Step by step solution

01

Step 1. Given information. 

The given expression is3log3x=log327

02

Step 2. Use logarithmic properties  

Using power property, we get:

3log3x=log327log3x3=log327

Using one to one property, we get:

x3=27

03

Step 3. Solve for x.   

Solving the equation, we get:

x3=27x=273cubingrootbothsidesx=3

04

Step 4. Check the value

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

3log3x=log3273log33=log327log333=log327log327=log327

This is true.

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

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