Question

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

Answer 1

Answer:

The condensed log equation is: $\log{\frac{x^4y}{z^5}}$

Step-by-step explanation:

We use these following logarithm properties to solve this question:

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

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

$\log{a} - \log{b} = \log{\frac{a}{b}}$

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:

$\log{\frac{x^4y}{z^5}}$

The condensed log equation is: $\log{\frac{x^4y}{z^5}}$