Question

Which property was used to rewrite log
https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAgLDBUexsJfHB.5rGOzcBm-rQDH5ZaE_3S2B/19809088,B84/Assets/assessmentimages/alg%202%20pt%202%20u4l4%2027.jpg

power property

power and quotient properties

quotient property

product and power properties

Answer 1

@Hero

Answer 2

0. Translation of Instructions: Re-write the given expression in the expected form, then identify the properties you used to arrive at the correct result.

Answer 3

I dont know how to do that @Hero

Answer 4

6 not 5

Answer 5

1. Rewrite the radical in fractional form.

Answer 6

how would i do that?

Answer 7

Apply the following rule, \(\sqrt[b]{x^a} = x^{a/b}\)

Answer 8

8x^3/6

Answer 9

If you're going to write horizontally, without LaTeX, you must use parentheses to clarify what in included in the exponent:
8x^(3/6)

Answer 10

2. Simplify the fraction.

Answer 11

what would i simplify

Answer 12

What does 3/6 simplify to?

Answer 13

1/2

Answer 14

So what would be the resulting expression after simplification?

Answer 15

8x/(3)

Answer 16

I suppose you misunderstood what 8x^(3/6) means

Answer 17

It means this: \(8x^{3/6}\) The 3/6 is an exponent by the way.

Answer 18

ok

Answer 19

One second, let me do this completely by hand first.

Answer 20

ok

Answer 21

Researching...

Answer 22

Sorry for taking so long. I made a silly mistake while going over this.

Answer 23

I'll just post the correct steps.

Answer 24

\(\begin{align*}\sqrt[6]{8x^3} &= \sqrt[6]{2^3x^3}\\&=\sqrt[6]{(2x)^3}\\&=(2x)^{3/6}\\&={2x^{1/2}}\end{align*}\)

Taking the log of that you get:

\(\begin{align*}\log{\left(2x^{1/2}\right)} &= \dfrac{1}{2}\log{(2x)}\end{align*}\)

Answer 25

so would this be the answer?

Answer 26

Well, it says to point out which property or properties of logs were used to get that result.

Answer 27

And there is only one property that was used. I guess that's your hint.

Answer 28

power property

Answer 29

is that right?

Answer 30

It's correct.

Answer 31

can you help me with 3-4 more?

Answer 32

Solve the question below.
https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAgtPT9McBUI1A.4lfcIf1WQczuX0l_mowc2C/19809088,B84/Assets/assessmentimages/alg%202%20pt%202%20u4l1%2015.jpg

400

505

399

506