# How do you use the properties of logarithms to write the expression log(9vx^8y^10/z^9)in terms of the logarithms of x,y, and z?

Jun 29, 2015

log(9vx^8y^10/ z^9) = log9 + logv +8logx + 10logy – 9logz

#### Explanation:

First Property: The logarithm of a product is the sum of the logarithms.

$\log \left(m n\right) = \log m + \log n$

Second Property: The logarithm of a quotient is the difference of the logarithms.

log(m/n) = logm – logn

So,

log(9vx^8y^10/ z^9) = log9 + logv + log(x^8) + log(y^10) – log(z^9)

Third Property: $\log \left({m}^{n}\right) = n \log m$

This gives

log(9vx^8y^10/ z^9) = log9 + logv + 8logx + 10logy – 9logz