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Find log (1 Viewer)
- Thread starter Drongoski
- Start date
Uncle
Banned
It's like saying:
4 to the power of (what) gives 8?
The (what) is 3/2
But,
The way to solve this because ya calculator probably only has log10 and ln, is to enter on your calculator:
log (8) / log (4)
use either ln or log10 it doesnt matter.
Then you get 3/2
capiche?
Uncle's right, I'll just fill in all the gaps if you treat it equating x.
Given log4 8 = x
The inverse function of a logarithm is the exponential function of the same base (in this case the 4). Therefore taking 4 to the power of each side:
4log4 8 = 4x
Therefore: 8 = 4x
Now you can take the logarithm of each side:
log (8) = log (4x)
Using your log rules allows you to take the x out as a factor:
log 8 = x log 4
Therefore:
x = ( log 8 ) / ( log 4 )
x = 3/2
Alternatively, if you are sharp enough to see that 4 cubed gives you 64 and the root of 64 is 8, then you can think your way straight to 43/2, therefore giving you 3/2 directly.
Best Regards
Herremann
addikaye03
The A-Team
gurmies
Drover
How I do it
I'm monitoring; waiting for any other approaches.
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Dunno, why you of all people would ask this...(unless there's something we don't know about? lol)
log48 = log4(4 x 2)
= log44 + log42
= 1 + log440.5
= 1 + 0.5log44
= 1.5
Trebla
There are exercises on logs/indices, even in yr 9 & 10 texts, such as finding: log8 16 and log9 27 and students often find them tricky. I'm curious to find out the various ways people approach such exercises. I'm already seeing quite a number of different ones, including yours and I find that interesting.
There are exercises on logs/indices, even in yr 9 & 10 texts, such as finding: log8 16 and log9 27 and students often find them tricky. I'm curious to find out the various ways people approach such exercises. I'm already seeing quite a number of different ones, including yours and I find that interesting.
Last edited:
addikaye03
The A-Team
haha sweet... our method is very efficient and a monkey could perform itHow I do it
Timothy.Siu
Prophet 9
i guess u could also do
log4 8=log 2 8/log 2 4=3/2
log4 8=log 2 8/log 2 4=3/2
addikaye03
The A-Team
ahh yes the old change of base... that old chestnut
Ok then, get your monkey and his method to evaluate: log736.
Best Regards
Herremann
Timothy.Siu
Prophet 9
easy, just tell it to do it on the calculator
addikaye03
The A-Team
Monkey: thats easy you noob,
log7 36=x
7^x=36
7^x=7^(ln36/ln7)
therefore x=ln36/ln7 or/ 1.841564442
Me: the monkey's pretty amazing
Monkey: Got anymore wise guy?
Me: Aww now your getting rude
You've skipped a few steps here that are going to confuse some people.
What I was pointing out was that your method is limited to simple indice-balancing questions. This works but denies students a deeper understanding of what logarithms are all about.
A simple:
7x = 36
log 7x = log 36 [taking logs]
x log 7 = log 36 [Using log laws]
x = log 36 / log 7
is the cleaner and more powerful method rather than muddying the water with equivalence of indices. As I was saying, leave that to the monkeys.
Best Regards
Herremann
hermand
je t'aime.
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drongoski said he was looking for different methods wise guy.
hermand
je t'aime.
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yes. that's the best way.Isn't it easier to say this:
???
haha, post this while you were bludging on maths? i knew it.