log questionsssssssss

Question

logbase2(x)+logbase2(2x)+logbase2(3x)+logbase2(36)=6

Answer 1

What is the question?

Answer 2

The logs have a common base of 2.  Also, we are adding the log terms.  So we need to multiply the arguments of the logs to compact them into a single log term.

 

log₂ (x * 2x * 3x * 36) = 6

 

log₂ (216x³) = 6

 

 

2⁶ = 216x³

 

2⁶ = 6³ x³

 

2⁶ = (2 * 3)³ x³

 

2⁶ = 2³ * 3³ * x³

 

2³ = 3³ x³

 

8 / 27 = x³

 

8 / 27 = x³

 

³√(8/27) = x

 

 

x = 2 / 3