Anonymous

# find log on a calculator?

how do i find log on my calculator i know i have a log button but i cant seem to figure out how to use it. im trying to find the value to log(subscript)2 64

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• Puggy
Lv 7

The problem with calculators is that you can't selectively choose a base with them. You either have to deal with base 10 (which is just the plain log button) or base e (which is the ln button).

All you have to do is recognize the change of base formula in math, which goes as follows:

log [ base c] (a) = (log [base b] (c) ) / (log [base b](a))

Translation: When calculating a certain log with base c, you can divide the log of what you're taking the log off with the log of the base itself, AND choose your own base. Because we're working with your calculator, you can choose either base 10 or base e.

Therefore, log [base 2](64) = (log 2) / (log 64)

HOWEVER, this is not how you should approach this problem; this problem is MEANT to be solved on paper, because of the relationship between 2 and 64.

Remember what log[base 2](64) is asking for; it's asking, "2 to the what power is equal to 64?" You have to solve this one algebraically, as using the calculator is only for approximations.

Let x = log [base 2] (64). Then, we have to convert this to exponential form.

To convert to exponential form, all you need to remember is that the BASE of the log becomes the BASE of the exponent. Then you just memorize everything else. So the equation becomes

2^x = 64

Now, it's important to note that 64 is indeed a power of 2 (2, 4, 8, 16, 32, 64, ...), in fact it's 2^6, therefore

2^x = 2^6

Which means you can now equate the exponents,

It's quite possible that on your calculator, you might get the value 5.9999999999999 or something funky. That's why it's a good idea to see if solving it algebraically is an option or not.

The following is a problem you would NOT solve algebraically:

2^x = 3

At this point, you'd convert it to logarithmic form, because nothing fits nicely. This becomes

x= log[base 2](3)

And using the Change of Base formula i described earlier

x = log(3) / log(2)

It is at THIS point you'd use your calculator to solve.

Remember that it doesn't matter whether you use log(3) / log(2) OR ln(3) / ln(2); they should both yield the same approximation.

I think (if I'm right) hes asking how to use the log buttons to find Log(base2) 64.

Log(base2) 64 = 6

Ln64 / Ln2 = 6

You have to find the Natural Log of 64 then divide it by the Natural Log of 2.

Hope that helps.

Look for a button that says log, lg or the equivalent value. There may be a need to use a shift key to obtain this feature. I would put the calculator model into Yahoo search and see what you can find!

• Anonymous
4 years ago

When possible, use properties... In this case it is possible. The property you must use is: The log of power of the base is the exponent... that is... in base 4 log(4^7) = 7 First you write (1/16) as power of 4.... (1/16)^3 = (4^-2) And now apply the property... (base 4) [log4^(-2)]^3 = [-2]^3 = -8 Ok!

Most calculators have a 'log' button which is log(sub)10 and/or a 'ln' button log(sub)e.

If your calculator is similar to mine, I don't have a log button to an arbitrary root.

You can use the relation however:

log(sub)a (x) = log(sub)b (x) / log(sub)b (a)

i.e. then log(sub)2 64 = log(sub)10 64 / log(sub) 10 2

= 1.80618 / .30103 = 6