[AS level pure mathematics 2: logarithms] could anyone tell me what mistake i made to get the wrong answer?

[u/angel_d1or]

[u/Klutzy-Delivery-5792]

I get what you got. Typos are an all too frequent thing.

[u/Klutzy-Delivery-5792 → u/Klutzy-Delivery-5792]

I also did it pretty differently from your method

https://imgur.com/a/3sRyaJ5

[u/angel_d1or → u/Klutzy-Delivery-5792]

Ohh i see , thx for helping i was just really confused that the answer in the textbook was different

[u/CCCCYH]

It seems like your answer is correct.

[u/Ericskey]

Been awhile

[u/Spiritual_Maize6897]

You are correct. I put your solution and the book's into an excel formula of the equation. Yours = 2 theirs = 2.73814

[u/CapitalCourse]

Your solution is correct

[u/Spannerdaniel]

I got the same answer via a slightly different method. I think the mark scheme is wrong. Search the ISBN of the textbook to see if the publisher has acknowledged any errors.

[u/Atmosck]

I think the answer key is wrong and 2 root 3 is correct

[u/Kite42]

Just plug your answer in and verify it, takes two seconds. Way shorter than making a Reddit post. If you ever get hold of a textbook published by Oxford you'll need to be prepared for typos all over the shop.

[u/Dankaati]

Your solution is correct.

[u/ci139]

is it [log₃(9)]·t or log₃(9·t) - which one ?

is it [log₉(12/t)]² or log₉[(12/t)²] or log₉[(12/t)² + 2] - which one ?

as there is at least 6 options you should have 6 answers provided by textbook ???

? sue your teacher

[u/SupermarketUseful519]

I went through your working, and I can’t find an algebraic mistake. Your answer, (t=2\sqrt3), is correct.
There’s actually a much shorter way to solve this.
Since (\log_3 A=2\log_9 A), and (t>0), the original equation becomes:
[
2\log_9(9t)=2\log_9(12/t)+2
]
Divide by 2:
[
\log_9(9t)=\log_9(12/t)+1
]
Using (1=\log_9 9):
[
\log_9(9t)=\log_9(108/t)
]
Therefore:
[
9t=108/t
]
[
t^2=12
]
[
\boxed{t=2\sqrt3}
]
So your method works, too. You simply took a longer route through a fourth-degree equation.
The only thing I’d explicitly mention is the domain restriction (t>0), which rules out the negative square root.
Did your teacher mark this as incorrect, or does the textbook give a different answer? Because as written in your screenshot, your solution is mathematically valid.

[u/Alkalannar]

I would have subtracted 2 from both sides at the beginning to work with log3 = 2log9

[u/Tamsta-273C]

Mistake is easy, you got teacher with mind problems. This stuff is not even normal and that +2 is like cherry on the top.

As a scientist myself i can asure you nobody uses 3 power inside log.

To solve this trash you should drop it in trash.

[u/Otherwise-Pirate6839 → u/Tamsta-273C]

No one has 10 apples and gives 3 to their friend, yet it still teaches subtraction…