wtire the expression

Question

Write the expression as a sum, difference, or multiple of logarithms. Assume that all variables represent positive real numbers.

 

 

1.  log₂ (√x/16) 

2. log₂  (x^3y^4 / 5)

3. log ₂ √16x

Answer 1

1)  log₂ √(x)  -  log₂ 16 = log₂ (x)^1/2  - 4  =  (1/2)log₂ (x) - 4

 

2)  log₂ x³  +  log₂ y^4/5 = 3log₂ x + (4/5)log₂ y

 

3)  log₂ 4x^1/2 = log₂ 4  +  log₂ x^1/2 = 2 + (1/2)log₂ x

Answer 2

Log₂(√x/16)

1/2Log₂(x) - Log₂(16)

 

Log₂(x³y⁴/5)

3Log₂(x) + 4Log₂(y) - Log₂(5)

 

Log₂√16x

1/2Log₂(16) + Log₂(x)