Question

!What is the value of log625^5 YOULL GET A MEDAL
a. -4
b. -1/4
c. 1/4
d. 4

Answer 1

\[\log(625^5)\]First pull out the 5 out front. This is a log rule dealing with powers. \[5\log(625)\]now tell me, is 625 a perfect square?

Answer 2

yea

Answer 3

it is

Answer 4

and what is it's square?

Answer 5

25

Answer 6

Good. So you now have \[5\log(25^2)\]We now do the same thing, can you tell me what will happen next if i use the power rule with this log function?

Answer 7

it will me 625 well yea or no

Answer 8

where will the power of 2 go?

Answer 9

hitn: follow the first step i presented you with.

Answer 10

on top of the 625 wouldnt it or 5

Answer 11

What are you saying...

Answer 12

Are you following what I am doing?

Answer 13

sorry im in a hurry cus its midnight at im sleepy but i need to finish this so im tired

Answer 14

\[5\log(25^2)\] we got 25^2 because, as you mentioned, 25^2 = 625, hence why I asked you if it is a perfect square.

Answer 15

yea

Answer 16

So as the power rule states, the 2 will come out front and multiply with the 5.\[5 \cdot 2 \log(25)\] 5 x 2 = 10 So we have \[10 \log(25)\]

Answer 17

25 is the perfect square of 5^2 so we can write log(25) as log(5^2)

Answer 18

So finally we will have \[10 \cdot 2 \log(5) =20\log(5) \]