Question

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?

Answer 1

`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(mn) = logm + logn`

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(m^n) = nlogm`

This gives

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