Properties of logarithms Write the expression as single loga

Properties of logarithms Write the expression as single logarithm. Simplify. Iog_2(x^2 - 25) - 3 log_2(x + 5) Write the expression as a sum and/or difference of logarithms. Express powers as factors. Log_2(x^5/x + 2), x>0

Solution

a) log₂(x^2 - 25) – 3log₂(x+5)

     = log₂(x - 5)(x+5) – 3log₂(x+5)

     = log₂(x - 5) + log₂(x + 5) - 3log₂(x+5)

     = log₂(x - 5) - 2 log₂(x+5)

     = log₂(x - 5) - log₂(x+5)^2

     = log₂[(x - 5)/(x + 5)^2]

b) log₂(x^5/(x+2)) = log₂ x^5 - log₂ (x+2)

   = 5 log₂ x - log₂ (x+2)