Question

CALCULUS/ Integration/ Volumes (Solids of revolution) - please help me :)
http://prntscr.com/5sp18c

Answer 1

i'm just unsure of how to make x the subject from y.

Answer 2

Yes! thats a good start

Answer 3

you may cancel logarithm by rising both sides 2 power

Answer 4

recall the fact that exponent undoes the log :
\[\large a^{ \log_a(x)} = x\]

Answer 5

I'm not too sure what that meant xD
Can you try to explain it again? ....

Answer 6

WAIT. i think i might have it?

Answer 7

lets see... let me ask you a silly exponent question first : \[\large 2^3 = ?\]

Answer 8

3 ?

Answer 9

nope

Answer 10

:O

Answer 11

Easy!
\[\large 2^3 = 2\times 2\times 2= 8\]

Answer 12

i thought you wanted me to identify the exponent? xD oops.

Answer 13

I see haha! let me as you a log question now :
\[\large 2^{?} = 8\]

Answer 14

what goes in question mark ?

Answer 15

3 ?

Answer 16

yes! so we say \(\large \log_2 (8) = 3\)

Answer 17

ohhhhh okay.
So would that mean x= 2^y ?

Answer 18

Yes!

Answer 19

okay, initially i had that but then i saw in part a that they wrote e^(yln4)
And i was just wondering how they got that part ??

Answer 20

so they're saying x^2 = e^(y ln4) but how did they get that? :O

Answer 21

square both sides

Answer 22

\[\large x= 2^y \implies x^2 = 2^{2y} = 4^y\]

Answer 23

@butterflydreamer since your only concern is how to write x in terms of y, as you stated in the opening remarks, here's a hint: Remember that\[e ^{\ln a}=a\]Does that help?

Answer 24

aaahh okay! @ganeshie8
@calculusfunctions Yup ! That helped ! Totally forgot that formula.

Answer 25

Perfect!

Answer 26

now use that formula in reverse to write \(4\) as \(e^{\ln 4}\)

Answer 27

yep! Okayyy that was really all i needed to understand xD
I will now proceed to work out the volume which i can do :)
THANK YOU BOTH VERY MUCH :D!

Answer 28

^^^with a y preceding ln 4

Answer 29

Yep rest of it is pretty straightforward and easy for you :)

Answer 30

thanks again :)

Answer 31

Welcome