How do you use the properties of logarithms to expand #log_10((xy^4)/z^3)#?

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Answer 1 · 2018-05-18T02:49:57

#=>log(x) + 4log(y) - 3log(z)#

There are few different properties that we can use here. I have listed them here:

[1] #log(ab) = log(a)+log(b)#

[2] #log(a/b) = log(a) - log(b)#

[3] #log(a^b) = blog(a)#

We are given:

#=>log((xy^4)/z^3)#

If we apply property [2], we get

#=>log(xy^4) -log(z^3)#

If we apply property [1] to the first term we get

#=>log(x) + log(y^4) - log(z^3)#

Now we can apply property [3] to all terms to get

#=>log(x) + 4log(y) - 3log(z)#