Question

Use the properties of logarithms to write the expression log(b) 4 sqrt(x^7 y^2/z^4) in terms of the logarithms x, y, and z.

Answer 1

The answer is 7/4 log(b) x + 1/2log(b) y - log(b) z, but I'm not sure how they arrived at it.

Answer 2

@Directrix

Answer 3

I think the Laws of Logs will be needed. Attached.

Answer 4

Will you post an image of the problem as it appears in your text? Thanks.

Answer 5

separate the "x", "y" and "z" and use the log laws someone has already posted.
when you multiply numbers/variables add the logs; when you divide numbers or variables you subtract the logs; the nth root is a fractional power; when you raise a power to a power you multiply the exponents