Question

What is log x + log y - 2 log z written as a single logarithm?

log2xyz
log xz^2/y
log 2z/xy
log xy/z^2

Answer 1

D) log (xy/z^2)

Explanation:

The given expression is log x + log y - 2 log z

Here we use log rules to simplify this.

Product rule: log x + log y = log (xy)

Quotient rule : log x - log y = log(x/y)

Power rule: log(x^y) = y.log(x)

Using the product rule

log x + log y - 2 log z

= log(xy) - 2 log z

Use the power rule now.

= log(xy) - log z^2

Now we have to use the Quotient rule and simplify.

= log
`(xy)/(z^(2) )`

Answer: D) log (xy/z^2)

Thank you.