Question

Logbase4x-logbase4(x-3)=3
Any help is appreciated!!!

Answer 1

x = 64/21

Explanation:

log_4 (x) - log_4(x-3) = 3

log_4 (x/(x-3)) = 3

64 = x/(x-3)

63x = 3 * 64

x = 64/21

Answer 2

• 
  `x = 64/21`

----------------------------

Use the identities below:

• 
  `log_a\ b\ - log_a\ c= log_a\ (b/c)`
• 
  `if\ log_a\ b=c\ then\ b=a^c`

Solve the equation:

• 
  `log_4\ x-log_4\ (x-3)=3`
• 
  `log_4\ (x/(x-3))=3`
• 
  `x/(x-3)=4^3`
• 
  `x/(x-3)=64`
• 
  `64(x -3)=x`
• 
  `64x-192=x`
• 
  `63x=192`
• 
  `x=192/63`
• 
  `x=64/21`