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?

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Answer 1 · 2015-06-29T18:03:22

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

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#