Question

how do u solve for r? 2112=42(r)^8

Answer 1

\[2112=42(r)^8\]

Answer 2

... is easier to read.

What would be your first step in solving this for r?

Answer 3

divide both sides by 42

Answer 4

@mathmale

Answer 5

Good thinking. Yes, that's what I'd do. Start with \[2112=42(r)^8\]

Answer 6

and divide both sides by 42. Your result?

Answer 7

50.28=r^8

Answer 8

Great. Let me ask you this: Have you already studied and used logarithms?

Answer 9

use but i dont know how to apply that here

Answer 10

yes*

Answer 11

Have you learned how to raise bases such as 10 to fractional powers, such as \[10^{1/2}\]?

Answer 12

i think but i dont quite remember

Answer 13

Good. Now, back to your first result: 50.28=r^8. We want to solve that for r.

One way to do that would be to take the 8th root of both sides of the equation:\[(50.28)^{1/8}=(r^8)^{1/8}\]

Answer 14

Are you able to do these operations on your calculator?

Actually, you don't need a calculator for the right side, since \[(r ^{8})^{1/8}=r ^{8/8}=r^1=r\]

Answer 15

What kind of calculator have you?

Answer 16

casio

Answer 17

scientific

Answer 18

Know how to evaluate 3^7 on your calculator?

Answer 19

yes

Answer 20

Know how to evaluate 3^(1/2) on your calculator? If so, find the approx value of 3^(1/2).

Answer 21

1.73

Answer 22

Hint: Be sure to enclose the exponent 1/2 in parentheses: 3^(1/2). Yes, that's correct.

Using this approach, can you evaluate \[50.28^{1/2}?\]

Answer 23

7.09

Answer 24

Great.

Now, one more. Can you evaluate \[50.28^{1/8}?\]

Answer 25

1.631

Answer 26

1.632

Answer 27

Be sure to enclose the 1/8 with parentheses. Yes, 1.631 is fine. That's your r value.

We used "fractional exponents" and "inverse functions" to obtain this result.

Answer 28

Want to go on to another problem, or want to solve this same problem in a different way, using logarithms?

Answer 29

No thanks for your help! :)

Answer 30

My pleasure. Take care.

Answer 31

You too :)