−9ln(x) − 4ln(y) + 1/4ln(z) assuming x, y and z are positive

Question

Assume that x, y and z are positive numbers. Use the properties of logarithms to write the expression below as the logarithm of one quantity.

−9ln(x) − 4ln(y) +1/4Ln(z)

Answer 1

Given -9ln(x)-4ln(y)+1/4ln(z)

Remember the logarithm properties.

a lnx = lnx^a

lnx+lny = ln(xy)

lnx-lny = ln(x/y)

-9ln(x)-4ln(y)+1/4ln(z)

= -lnx^9-lny^4+lnz^1/4

= -(lnx^9+lny^4)+lnz^1/4

= -lnx^9y^4+lnz^1/4

= lnz^1/4-lnx^9y^4

= ln(x^9y^4/z^1/4)

Answer 2

Recall the properties of logarithms