SOLUTION: Hi, this is my first time asking a question :D If {{{ log( 2, 12 ) }}} = a , find {{{ log( 2, 18 ) }}} in terms of a. I tried to break down {{{ log( 2, 18 ) }}} to something

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi, this is my first time asking a question :D If {{{ log( 2, 12 ) }}} = a , find {{{ log( 2, 18 ) }}} in terms of a. I tried to break down {{{ log( 2, 18 ) }}} to something       Log On


   

Question 891923: Hi, this is my first time asking a question :D
If +log%28+2%2C+12+%29+ = a , find +log%28+2%2C+18+%29+ in terms of a.
I tried to break down +log%28+2%2C+18+%29+ to something like +log%28+2%2C+216%2F12+%29+ . Then, +log%28+2%2C+216+%29+ - +log%28+2%2C+12+%29+ so that it can be simplified to +log%28+2%2C+216+%29+ - a . But I couldn't do anything more. I tried other ways but this method seemed to be the best.
The answer says 2a - 3 but it does not provide any explanation. Could you guide me through this question?
I tried to work it out backwards using this answer 2a - 3. I got +log%28+2%2C+144+%29+ - 3 . Then +log%28+2%2C+144+%29+ - +log%28+2%2C+8+%29+. And finally +log%28+2%2C+144%2F8+%29+ which gives me +log%28+2%2C+18+%29+. Supposing I did not know the answer, how can I work it out to get 2a - 3? Thank you in advance.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Answer is 2a-3.
Tricky, but here is the trick.......

log%282%2C12%29=a
a=log%282%2C2%2A2%2A3%29
log%282%2C%28%282%5E2%29%2A3%29%29
log%282%2C2%5E2%29%2Blog%282%2C3%29
2%2Alog%282%2C2%29%2Blog%282%2C3%29
2%2Blog%282%2C3%29=a
highlight_green%28log%282%2C3%29=a-2%29---This is what you will use.

Now Starting at log%282%2C18%29,
log%282%2C%282%2A3%5E2%29%29
log%282%2C2%29%2Blog%282%2C%283%5E2%29%29
1%2B2%2Alog%282%2C3%29-----You simply substitute what you just found for log%282%2C3%29 !
.
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