Question

2 log x - log y - 2 log z as a single logarithm

Answer 1

`log(x^2)/(yz^2)`

Explanation:

Simplify 2log(x) by moving 2

inside the logarithm.

Simplify 2log(x) by moving 2

inside the logarithm.

log(x^2)−log(y)−2log(z)

Simplify −2log(z)

by moving 2

inside the logarithm.

log(x^2)−log(y)−log(z^2)

Use the quotient property of logarithms, logb (x)−logb (y)=logb (x/y)

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

Use the quotient property of logarithms, logb(x)−logb(y)=logb (x/y)

`log ((x)/(y))/( (1)/(z^2)}]`

Multiply the numerator by the reciprocal of the denominator.

`log(x^2\\ )/(y).(1)/(z^2)`

Combine.

`log(x^2*1\\ )/(yz^2)`

Multiply
`x^(2)` by 1

`log(x^2)/(yz^2)`

Answer 2

log ( x^2/(yz^2))

Explanation:

2 log x - log y - 2 log z

We know a log b = log b^a

Rewriting

2 log x = log x^2 and 2 log z = log z^2

log x^2 - log y - log z^2

Rewriting

log x^2 - (log y + log z^2)

We know that log a + log b = log (a*b)

log x^2 - (log (y z^2))

And we know log a - log b = log (a/b)

log ( x^2/(yz^2))