+0

# Solving logs by formula and not a calculator.

0
607
9
Ok, can you (somebody) help me to understand log function- converting to base 10. And how to manually calculate in non base ten given equation and formula. I have the formulas but unsure the process exactly as my notes left me a bit confused. And sorry, I've not really looked at vids on this atm as I'm really trying to focus on conic sections and graphing for my study atm. Just want to re-go over the calculating part of logarithms, thus making sure I can understand it. the information here will be the best to achieve this.
Feb 17, 2014

#1
0
log b(x) = log c(x) / log c(b)

so

log 10(x) = log c(x) / log c(10)
Feb 17, 2014
#2
0
That isn't that clear to me Rom. Also I'm unsure which part of the question you're answering specifically. Though I feel it's conversion process for any log function into a base 10 log. But it seems alien and a bit backwards, though I'm sure it's not.
Specifically, this does not expalin to me how it goes from a log 4 function to a log 10 function, or how to calculate a log 4 function manually, in steps (since I have the problems and the fomulae but not the method) and It does not really explain what is x b and c, where we have one equation, what's what.

logb(x) = logc(x) / logc(b)

so

log10(x) = logc(x) / logc(10)
If you could explain it a bit more thanks.

My interpretation would be logb is log input any base and it will be calculated by log original base by log new base. And what about powers? And how do we solve for powers? What's the step from log 2 or 4 or 7 etc.

Still would like to know the calculation method to manually calculate for example log 478. and maybe you can show a little bit of a more difficult log problem and solve to show me also. But I'd like to know the method of working through it specifically and where powers are involved. Ie. what's being Sqrt'ed, multiplied, divided etc to come up with an answer if any one would like to help.
Feb 17, 2014
#3
0

log 4(78) = log 10(78) / log 10(4)

Now you talk about calculating these things manually. I'm not entirely sure what you mean by that. Even for base 10 logs eventually you're going to be reduced to one of 3 ways of getting the actual value

a) punching the buttons on your calculator
b) looking the value up in a table
c) approximating it by it's series or perhaps some other approximation formula

unless of course the argument is a power of the base in which case the log is just that power, for example

log 10(1000) = log 10(10 3) = 3
log 4(1024) = log 4(4 5) = 5

without using one of the methods a-c above about the best you can do is note that

4 3 = 64 < 78 < 256 = 4 4

and thus 3 < log 4(78) < 4

back in the old days before electronic calculators (and yes I was alive back then) all we had was tables of base 10 logs and every problem involving logs first had to be converted to base 10 using the formula I gave you, and then done in base 10 and converted back if necessary. With pencil and paper (or a slide rule if you had one).

If you're interested in the series I'm referring to in (c) above you can read about it here. http://en.wikipedia.org/wiki/Logarithm#Calculation
Feb 17, 2014
#5
0
solve log 4(1/4).. What do I do with the fraction in a log situation. How in the instance described do I apply log am n = n log am. Oh It should be so easy. Got to work out some of the nuts and bolts I think with this one.

and working this to: 2 log a5 + log ap
Feb 19, 2014
#6
0
Quote:

log4(1/4)

*cough*

1/4 = 4 (-1)

so log 4(1/4) = -1
Feb 19, 2014
#7
0
Stu:

solve log4(1/4).. What do I do with the fraction in a log situation. How in the instance described do I apply logamn = n logam. Oh It should be so easy. Got to work out some of the nuts and bolts I think with this one.

and working this to: 2 loga5 + logap

Hi Stu,
Remember this stuff that we did before Stu.
http://web2.0calc.com/questions/viewtopic.php?f=2&t=8007&p=18073&hilit=negative+indices#p18073
take a look and revise.

now 1/4 = 1/4 1 ==> 4 -1
Remember that Stu? Probably not, I know that you have been swamped.
so
log 4(1/4) = log 4(4 -1) ==> -1*log 44 ==> -1*1 ==> -1
------------------------------------------------------------------------------------------------

2 log a5 + log ap =

= log a5 2 + log ap

= log a25 + log ap

= log a(25p)

http://en.wikipedia.org/wiki/List_of_logarithmic_identities
Feb 19, 2014
#8
0
Yeh, I knew it was simple. lol. I even went over this yesterday in a different example to flip the fraction which came to me after posting. Thanks for the reply. lol. Still have to absorb it, enough to remember all, apply as needed and enough to do method in reverse. It's a slow process when it's all new.