Use properties of logarithms to expand the logarithmic expre

Use properties of logarithms to expand the logarithmic expression, and simplify if possible. log_5 (squareroot x/125)

Solution

log₅[x^(1/2)/125]

= log₅x^(1/2) - log₅125

= log₅x^(1/2) - log₅5^3

= (1/2)log₅x - 3*log₅5

= (1/2)log₅x - 3*1

= (1/2)log₅x - 3

Used properties:

log (m/n) = log m - log n

log (m^n) = n*log m

log_nn = 1