Question

Condense the log equation: 4 log x + log y - 5 log z

Answer 1

The condensed log equation is:
`\log{(x^4y)/(z^5)}`

Explanation:

We use these following logarithm properties to solve this question:

`a\log{x} = \log{x^a}`

`\log{a} + \log{b} = \log{ab}`

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

In this question:

`4\log{x} = \log{x^4}`

`5\log{5} = \log{z^5}`

So

`4\log{x} + \log{y} - 5\log{z}`

Becomes:

`\log{x^4} + \log{y} - \log{z^5}`

Now applying the addition and subtraction properties, we have:

`\log{(x^4y)/(z^5)}`

The condensed log equation is:
`\log{(x^4y)/(z^5)}`