How do I get log 10 of any number? - HP 12c Calculator

Calculate the log (base 10) of the number, then divide the result by the log (base 10) of the base.
For example, to calculate the base-3 log of 9, calculate the log of 9 to get 0.954 . Divide that by the log of 3 (about 0.477) to get 2.0 .
Since 9 is 3 squared, the log base 3 of 9 is 2, as we just calculated.

To calculate the common log ( LOG base 10) of a positive number, just press the LOG key, the one above the blue Division key, then enter the number and close the right parenthesis. Press the ENTER key to get the result.

If you want to calculate the log in a base other than e (natural) or 10 (decimal) logarithms, you need to make use of one of the equivalent formulas below

log in base a of a number b
log_a(b)=log_10(b) / [ log_10(a)] or
log_a(b)= ln(b)/ln(a)

The BA II+ does not have a key for the common logarithm function. You can calculate the common log of a number by calculating its natural log and then dividing by the natural log of 10.

log10(x) = ln(x)/ln(10)

The same procedure works for logarithms to any base.

The answer for the problem log(4) - log(2) is actually 0.301, so the good news is that your calculator is working properly! Here's a quick breakdown of the solution for the problem:

1) We know that log(x) = N means that 10^N = x. So in this case, we need to find a number that 10 can be raised to in order to get 4 and 2.
2) To get a better idea of what the answer to the problem will be, we look at the scale of the numbers. 4 and 2 are both smaller than 10. In order to raise any number to a power and get a smaller number, that power must be less than 1. If the power was 1 or greater, the answer would be more than 10. Therefore, we know that log(4) is a decimal less than 1 and log(2) is a decimal less than 1.
3) Now we'll simplify the problem. A logarithm rule states that:

log(x) - log(y) = log(x/y)

We can use this rule to simplify the equation in the problem.

log(4) - log(2) = log(4/2)

Since 4/2 = 2,

log(4) - log(2) = log(4/2) = log(2)

4) Now to solve the equation, the only thing that must be calculated is log(2). This would be done on a calculator. In step 2, we analyzed that log(2) must be less than 1. Therefore, the calculator is correct with the answer 0.301.

Hope this helped!

The conversion formula is
# dB =10*log(Pout/Pin) for say an amplifier.
For your case
Pout/Pin= 10^4 then #dB =10*log(10^4)=10*4=40 dB

Let us take a less obscure exemple

# dB= 57.39, what is the power ratio?
10*log(Pout/Pin)= 57.39
log(Pout/Pin)=57.39/10=5.739
Pout/Pin=Ratio =10^(5.739)= 548276.9649, not a number you would hear or see quoted, but a correct value.

To calculate the power ratio

1. Convert the decibels in Bels (divide by 10)
2. While the number just calculated is still in Answer memory (ANS), press [SHIFT] [LOG] to access the the 10^x function
3. Press [SHIFT][(-)] to enter (ANS)
4. Close the parenthesis [)]
5. Press [ENTER]

Here is the screen capture for the calculation one way and back.

Hi,

Logarithms in base 10 :Common logarithms

1. The calculator has a key labeled [LOG]. It allows you to calculate the common logarithms (logarithms in base 10).
2. To calculate the common logarithm of a (positive) number you type in the number, press the [LOG] key .
3. Ex: 15.32 [LOG][=] gives 1.1852558765

Logarithms in base e : Natural logarithms

1. The calculator has a key labeled [LN]. It allows you to calculate the natural logarithms of positive numbers.
2. Ex: natural log of 15.32 is entered as
3. 15.32 [LN] gives 2.729159164

Hope it helps.
Don't forget to rate the solution and don't be stingy: 4 thumbs up won't leave you any the poorer.

Hello,
Why complicate matters for yourself?
You were asked to calculate log(6.02x10^23), let your finger do the calculating.
I checked the claculator manual and you have to enter it all at one go. Pay attention to the key strokes. You will not do it in such a laborious manner

23[10^x] [=] gives 10^23
23[10^x]*6.02 [=] multiplies 6.02 by 10^23 to give you Avogadro s number.

To find its logarithm in base 10, you have to enter the number then press [LOG] . When you press [LOG] you are calculating the log of the last result. You obtain 23.77959649.

If I had given you the key strokes directly you might have not understood why I do things this way. Now the actual key strokes you enter

23[10^x] * 6.02 [LOG] [=]

If you are only looking for your result, you are done. You can ignore what follows.

If you know the rules for the logarithms, you can do the calculation more easily. log here is log in base 10

Rule 1 Log(a*b)= log(a) + log(b)
Rule 2 Log(c^n) = n* log(c)
Rule 3 log(10)=1

Thus applying the rules
log(6.02*10^23) = log(6.02) + log(10^23) first rule applied
= log(6.02) + 23*log(10) 2nd rule applied
= log(6.02) + 23 3rd rule applied
= 0.77959649 + 23= 23.77959649
Hope it helps

Hello,
To calculate the natural log of a number use [LN] key. You enter it as
number [LN] [=] exemple 15.32 [LN] [=] gives 2.729150164
To clculate the log base 10 (common logarithm) you use the [LOG] key
15.32 [LOG][=] gives 1.185258765.

Hope it helps

Hello,
If you know the theory skip this and go to Application
Let y=10^(x) 10 to the power of x
Take the log of both tems of the equality. You get
log(y)=log[10^(x)] where I used square brackets for clarity. But from the general properties of logarithms

log(b^(a)) = a*log(b)
Applied to our expression above
log(10^x)=x*log10
But since we are using log as log in base 10, log_10(10)=1
so
log(y)=x
We thus have two equivalent relations
y=10^x <----> x=log(y) The double arrow stands for equivalence.

If y is the log of x, then x is the antilog of y

Application: What is the antilog of 3.76?
antilog of 3.76 =10^(3.76) = 5754.399373
Take the log in base 10 of this number and you recover 3.76

You enter it as follows
10[^]3.76[ENTER/=] gives 5754.399373
And log(5754.399373)= 3.76

Hope it helps

"♦" "7" will give you log base 10 for the texas instuments TI-89 Titanium