Question

What is the equation written as a single
Logarithm

Answer 1

Choice 3

`log (x^2y)/(z^2)`

Explanation:

We use 3 of the rules of logarithms

• Product Rule :

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

• Quotient Rule:

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

• Power Rule

`\log (a^n) = n\log a`

`\log(x^2y)/(z^2) =\ log(x^2y) - \log(z^2)` (quotient rule)

`\log(x^2y) = \log x^2 + \log y` (product rule)

`\log x^2 = 2\log x` (power rule)

`\log z^2 = 2\log z` (power rule)

Final result

`log (x^2y)/(z^2) = 2\log x + \log y - \log z`