C2 Logarithms Question?

Given that
log a Y= 2log a 3+ log a 4+1
express y in terms of a, giving your answer in a form that does not involve logarithms.

log a = log to the base of a (log small a)

I got Y to be 45 but I don't know how to work out a, any advice? Thanks

Reply 1

Andy98

20

Original post by Megan_101

Given that
log a Y= 2log a 3+ log a 4+1
express y in terms of a, giving your answer in a form that does not involve logarithms.

log a = log to the base of a (log small a)

I got Y to be 45 but I don't know how to work out a, any advice? Thanks

Can I see your working?

y

should come out as

ma^n

where m and n are constants. You don't need to find a, in fact you can't without more information. So I'm not sure how you got

y=45

Reply 2

math42

20

Original post by Megan_101

Given that
log a Y= 2log a 3+ log a 4+1
express y in terms of a, giving your answer in a form that does not involve logarithms.

log a = log to the base of a (log small a)

I got Y to be 45 but I don't know how to work out a, any advice? Thanks

Y should be found in terms of a, rather than as a specific value.

Reply 3

Razzamataz179

8

Group the right hand side first, remember your logarithm rules, and change 1 into a logarithm in terms of a (hint: log 10 (10) = ?). Then all the logs will cancel.

Reply 4

B_9710

18

Original post by Megan_101

Given that
log a Y= 2log a 3+ log a 4+1
express y in terms of a, giving your answer in a form that does not involve logarithms.

log a = log to the base of a (log small a)

I got Y to be 45 but I don't know how to work out a, any advice? Thanks

You won't be able to work out an actual value for y. Just an expression for it in terms of a

Reply 5

B_9710

18

Treat the + 1 on the RHS as loga (a)
Meaning log to the base a of a

Reply 6

Megan_101

OP

4

Original post by Andy98

Can I see your working?

y

should come out as

ma^n

where m and n are constants. You don't need to find a, in fact you can't without more information. So I'm not sure how you got

y=45

logaY= loga9+loga4+1
logaY=loga(9x(4+1))
logaY=loga45
Y=45
Maybe you can't add the 4 and 1 then?

Reply 7

Megan_101

OP

4

Original post by 1 8 13 20 42

Y should be found in terms of a, rather than as a specific value.

I didn't intend to find Y, I just started simplifying it and then I got the value of Y

Reply 8

Andy98

20

Original post by Megan_101

logaY= loga9+loga4+1
logaY=loga(9x(4+1))
logaY=loga45
Y=45
Maybe you can't add the 4 and 1 then?

Ahhhh I see where you went wrong.

From what I see the 1 isn't part of the log, simplify all the logs and raise everything to the exponent.

Reply 9

Megan_101

OP

4

Original post by Razzamataz179

Group the right hand side first, remember your logarithm rules, and change 1 into a logarithm in terms of a (hint: log 10 (10) = ?). Then all the logs will cancel.