Write the expression as a logarithm of a single expression S

Write the expression as a logarithm of a single expression. Simplify the final answer if possible. In 4squareroot 5 - ln 25 In squareroot 5 - ln 25 = In (___________) (Simplify your answer.)

Solution

given ln(5)^1/4 - ln(25)

ln [ (5)^1/4/25 ] [ since ln a - ln b = ln(a/b)

ln [(5)^1/4/5² ]

ln [ (5)^{1/4 - 2}]

ln [ (5)^-7/4 ]

or

-7/4 ln(5)