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Chapter 10: Q. 295 (page 1054)

In the following exercise, solve for x.

log4x+log4x=3

Short Answer

Expert verified

The solution of the given expression isx=9

Step by step solution

01

Step 1. Given information.

The given expression islog4x+log4x=3

02

Step 2. Use logarithmic properties      

Using product rule, we get:

log4x+log4x=3log4x路x=3log4x2=3

Writing it in exponential form, we get:

x2=34x2=81

03

Step 3. Solve for x.   

Solving the equation, we get:

x2=81x=卤81x=卤9

We eliminate x=-9as the logarithmic function doesn't take any negative values.

04

Step 4. Check the value   

Substituting x=9in the given expression, we get:

log4x+log4x=3log49+log49=3log49路9=3log481=23=3

This is true.

Thus, x=9is the solution of the given function.

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