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# this logs question is really annoying me.. help! Watch

1. hey there

I have a question and theres one part of it that just is not making any sense

"Find the exact values of x and y given that logyx=3 and Log3x-log3y=5"

okay so I did:
logyx=3
y3=x

log3x-log3y=5
log3x/y=5
Log3y2=5
y2=35
y=35/2 <---why can we take the 2 from the left and divide it by the five? I didn't know we could do this

when I sub y=35/2 in y^3=x i get 3788 and not the answer of 3^(15/2) which it says on the mark scheme

any ideas anyone? thank you
2. (Original post by upthegunners)
hey there

I have a question and theres one part of it that just is not making any sense

"Find the exact values of x and y given that logyx=3 and Log3x-log3y=5"

okay so I did:
logyx=3
y3=x

log3x-log3y=5
log3x/y=5
Log3y2=5
y2=35
y=35/2 <---why can we take the 2 from the left and divide it by the five? I didn't know we could do this

when I sub y=35/2 in y^3=x i get 3788 and not the answer of 3^(15/2) which it says on the mark scheme

any ideas anyone? thank you
....

a^2 = x

a = x^(1/2)
3. (Original post by upthegunners)
hey there

I have a question and theres one part of it that just is not making any sense

"Find the exact values of x and y given that logyx=3 and Log3x-log3y=5"

okay so I did:
logyx=3
y3=x

log3x-log3y=5
log3x/y=5
Log3y2=5
y2=35
y=35/2 <---why can we take the 2 from the left and divide it by the five? I didn't know we could do this

when I sub y=35/2 in y^3=x i get 3788 and not the answer of 3^(15/2) which it says on the mark scheme

any ideas anyone? thank you
y=35/2 in y^3=x << this equals y=315/2

simple 5 x 3

oh and if you put 3^7.5 in your calculator you get 3788

ryan
4. (Original post by ryanb97)
y=35/2 in y^3=x << this equals y=315/2

simple 5 x 3

ryan
is the rule of indices not that (5/2)3 = 125/8 ?
5. (Original post by 2710)
....

a^2 = x

a = x^(1/2)
how does this work? I dont remember ever learning this indices rule
6. you have (keep it in this form):

so, take the square root of 81 x 3 =

sub that (each) into x=y^3
7. (Original post by upthegunners)
is the rule of indices not that (5/2)3 = 125/8 ?
That is one rule of indices

Another (more relevant here) is that
8. (Original post by upthegunners)
how does this work? I dont remember ever learning this indices rule
The rule that squaring is the opposite of square rooting

I think you probably have learnt that
9. (Original post by TenOfThem)
That is one rule of indices

Another (more relevant here) is that
thanks so much!

So what is the rule that would allow me to cube it?
10. (Original post by upthegunners)
how does this work? I dont remember ever learning this indices rule
It's the rule of square roots,
then
11. (Original post by Robbie242)
It's the rule of square roots,
then
I always thought that if a fraction was raised to the power 3 you cubed both the numerator and the denominator
12. (Original post by upthegunners)
I always thought that if a fraction was raised to the power 3 you cubed both the numerator and the denominator
Depends what fraction if the numerator>1 or <-1 then it will have an effect, if it is =1 or -1 then it will have an effect as (-1)^3=-1. In short I just just cube it so
13. (Original post by Robbie242)
Depends what fraction
how can it be different?

A fraction is a fraction
14. (Original post by upthegunners)
hey there

I have a question and theres one part of it that just is not making any sense

"Find the exact values of x and y given that logyx=3 and Log3x-log3y=5"

okay so I did:
logyx=3
y3=x

log3x-log3y=5
log3x/y=5
Log3y2=5
y2=35
y=35/2 <---why can we take the 2 from the left and divide it by the five? I didn't know we could do this

when I sub y=35/2 in y^3=x i get 3788 and not the answer of 3^(15/2) which it says on the mark scheme

any ideas anyone? thank you
From the identities of

and

SO
y^2=3^5
taking squre root

Similarly
15. (Original post by upthegunners)
how can it be different?

A fraction is a fraction
yes I mean if it were 1 then cubing it would not alter it at all, but yes your right a fraction is indeed a fraction
16. (Original post by upthegunners)
I always thought that if a fraction was raised to the power 3 you cubed both the numerator and the denominator
You do...
17. (Original post by 2710)
You do...
then why not in the original case?
18. (Original post by upthegunners)
then why not in the original case?
Which original case? I dont see any fraction?

y^2=3^5

y = 3^(5/2)

Wheres the fraction u are talking about?
19. (Original post by upthegunners)
then why not in the original case?
Because you are not raising a fraction to a power
20. Oh i see. Because as above has said, you are not raising the fraction to a power if u look carefully

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