Question

Part 1: Is the following equation true? (2 points)

Part 2: Use complete sentences to explain the properties used in making your decision. (6 points)

2 log 5 x + one–half log 5 y – 4 log 5 z = log 5 x-squared times square root of y all over z to the fourth power.

Answer 1

Let's try to type in the formula you have:

\(2\log_{5}x+\frac{1}{2}\log_{5}y-4\log_{5}z=\log_{5}\dfrac{x^2\sqrt{y}}{z^4}\).

Answer 2

The rules you have to use are:

1. \(k \cdot \log_{a}b=\log_{a}b^k\)
2. \(\log_{a}b+\log_{a}c=\log_{a}bc\)
3. \(\log_{a}b-\log_{a}c=\log_{a}\dfrac{b}{c}\)

Answer 3

The easy question is Part 1: if you look at the rules, you can see that the equation must be true.

To use complete sentences to explain seems like torturing to me :(

Answer 4

To see that it is true, write it like this first: (using rule #1)

\(\log_{5}x^2+\log_{5}y^{\frac{1}{2}}-\log_{5}z^4\).

Answer 5

Now remember that \(y^{\frac{1}{2}}=\sqrt{y}\)and use rules #2 and #3, to arrive at the right hand side of the equation.