In both Chemistry 1 and 2 you will see plenty of logarithms.
In fact they are part of a lot of formulas, so let's review what logarithms and natural logarithms are.
Note we can call logarithms logs for short and natural logarithms can be referred to as ln.
Logs are another way to think about exponents.
For example we know that 10 squared is 100.
We could rewrite this as a logarithm where the base 10 goes here,
the 100 or whatever the left side equals goes with the log, and our exponent is set equal to all of this.
This is the generic form of a log called logarithmic form and the generic form of it's exponent is called exponential form.
You will need to know how to switch back and forth from logarithmic form to exponential form and vice versa in a specific way in Chemistry.
In Chemistry we will only be dealing with logs that have a base of 10,
which is also what your calculator allows for.
This is why the base 10 will not be shown in any of the formulas or questions, know that this base is always 10.
We will see this a lot whenever we are talking about acids and bases.
Taking the log of a value is very simple since you have to use your calculator.
Let's say we were asked to find the pH of this acid concentration.
Where the formula for pH is equal to negative log of the acid concentration.
So all we would do is plug in our value and plug this into our calculator,
so for a scientific calculator we would start with the number 2.8 then press EE since this is the same as this part of our number in scientific notation and enter a negative 4.
Next press the log button, press the negative button to account for this negative sign.
The pH is 3.55.
You will see this same type of formula a lot in Chem 1 and 2.
Let's take the log of a fraction.
You will use this type of equation in Chem 2 when you are asked to find the pH of a buffer.
Let's say this was your equation with all the values needed.
When taking the log of a fraction know that whatever is next to a log is actually in parentheses.
So we need to do what is in parentheses first,
then take the log of this value and continue with this formula to get this answer.
Taking the natural log of a value is very similar.
You would still do whatever is in parentheses first if necessary then take the ln of this value and continue with this rest of the formula.
Where it starts to get a little bit tricky is when you need to cancel out a log or natural log to get the formula back to exponential form.
This next part is very important!
To cancel out a log with a base of 10, you take the anti-log of both sides which is really just taking the base 10 of both sides.
The logs cancel and you are left with a value and this is now an exponent.
Let's try this with pH.
If we wanted to find the acid concentration and were given the pH here's what we'd do.
Using the pH formula, start with dividing over the -1 in front here to both sides.
Now we can take the anti-log of both sides, the log and base 10 cancel out and we can rewrite this as the acid concentration is equal to 10 raised to the - pH.
To do this on a scientific calculator,
plug in the exponent first of -1, enter the number then press the negative sign then press 2nd log and this is our value.
Here's another example.
We will solve for this unknown variable.
Start with getting the log by itself by subtracting both sides by 4.77.
Now that the log is isolated we can take the anti-log of both sides.
The logs cancel out and this fraction comes down while this now becomes an exponent.
To do this on a scientific calculator,
plug in the exponent first of 0.04 enter the number then press the negative sign then press 2nd log and this is our value,
to finish this question we will multiply both sides by 0.5 and get this as our answer.
To cancel out a natural log we raise both sides of the equation by it's base which is e.
We would use this when using this equation and we were asked to solve for one of these pressures.
Let's review the math.
All values are plugged in and we'll solve for P2.
Start with the right side, calculate each fraction then subtract.
Next divide these two values and multiply.
Now that we combined everything on the right side we can solve for P2.
Recall that we are not allowed to separate P2 from the ln,
since this fraction is actually in parentheses.
Instead we will cancel out ln first by taking the e of both sides.
The ln and e cancel out to leave just the fraction and we can drop the parentheses.
On the right side we get e raised to this power.
To find this using a scientific calculator, plug in the exponent first by entering the number then press the negative sign then press 2nd log and this is our value.
Some rules and properties to know for logs and natural logs are these.
Rule 1 You are not able to take the log or natural log of zero.
Rule 2 You are not able to take the log or natural log of a negative number.
This is why your calculator will say error if you try to do this.
If for some reason you get a concentration or value that is a zero or a negative this is a way to check yourself and see that a mistake was made in your previous calculation.
This next property is whenever you take the log or ln of a number with an exponent, the exponent comes down in front of the log or ln.
For example, if you were trying to solve for x here,
the only way to do this is by taking the ln of both sides since this is in exponential form.
By taking the ln of this number with an exponent,
the exponent will come down in front of the ln and you would continue to solve this question by isolating x.
You can take the ln of each value separately then divide by the new value to get x.
You will see examples like this in Chemistry 2 specifically when you are finding the rate law.
Of course these were just some examples you will see Chemistry,
for different examples, click the link in the description to be even more prepared for this class.
Once you finish those practice problems come back for the next video in this playlist.