Question

The expression can be written in the form

Answer 1

• A = 8
• B = 19
• C = -17

Explanation:

You want the values of A, B, C in A·log(x) +B·log(y) +C·log(z) = log(x^8y^19/z^17).

Rules of logarithms

It is helpful to remember that ...

log(ab) = log(a) +log(b)

log(a/b) = log(a) -log(b)

log(a^b) = b·log(a)

Application

`\log{\left((x^8y^(19))/(z^(17))\right)}=\log(x^8)+\log(y^(19))-\log(z^(17))\\\\=8\log(x)+19\log(y)-17\log{z}`

A = 8, B = 19, C = -17

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