Find log (1 Viewer)

[Drongoski]

Show how u find:

log₄ 8 ?

 

[Uncle]

Show how u find:

log₄ 8 ?

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?

 

[Herremann]

Show how u find:

log₄ 8 ?

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:

4^{log₄ 8} = 4^x

Therefore: 8 = 4^x

Now you can take the logarithm of each side:

log (8) = log (4^x)

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 4^3/2, therefore giving you 3/2 directly.

Best Regards
Herremann

 

[addikaye03]

Show how u find:

log₄ 8 ?

log4 8 = x

4^x=8

(2)^2x=2^3

therefore by equating indices of equal bases

x=3/2

 

[gurmies]

log4 8 = x

4^x=8

(2)^2x=2^3

therefore by equating indices of equal bases

x=3/2

How I do it

 

[Woteva636]

its called the change of base rule, i cant find my text book so i cant really explain it, but i thought he others had done it pretty well.

 

[Drongoski]

its called the change of base rule, i cant find my text book so i cant really explain it, but i thought he others had done it pretty well.

I'm monitoring; waiting for any other approaches.

 

[Trebla]

Show how u find:

log₄ 8 ?

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 + log₄4^0.5
= 1 + 0.5log₄4
= 1.5

 

[Drongoski]

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.

 

[addikaye03]

How I do it

haha sweet... our method is very efficient and a monkey could perform it

 

[Timothy.Siu]

i guess u could also do

log₄ 8=log ₂ 8/log ₂ 4=3/2

 

[addikaye03]

i guess u could also do

log₄ 8=log ₂ 8/log ₂ 4=3/2

ahh yes the old change of base... that old chestnut

 

[Herremann]

haha sweet... our method is very efficient and a monkey could perform it

Ok then, get your monkey and his method to evaluate: log₇36.

Best Regards
Herremann

 

[Timothy.Siu]

Ok then, get your monkey and his method to evaluate: log₇36.

Best Regards
Herremann

easy, just tell it to do it on the calculator

 

[addikaye03]

Ok then, get your monkey and his method to evaluate: log₇36.

Best Regards
Herremann

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

 

[Herremann]

...7^x=36

to

7^x=7^(ln36/ln7)...

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:

7^x = 36
log 7^x = 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]

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:

7^x = 36
log 7^x = 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

drongoski said he was looking for different methods wise guy.

 

[bell531]

Isn't it easier to say this:



???

 

[hermand]

Isn't it easier to say this:



???

yes. that's the best way.

haha, post this while you were bludging on maths? i knew it.

 

[bell531]

I'm only late when I want to be...