ACT Math : How to find a logarithm
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Example Question #11 : Logarithms
What is the value of 
You could solve this by using your calculator. Remember that you will have to translate this into:
Another way you can solve it is by noticing that
This means you can rewrite your logarithm:
Applying logarithm rules, you can factor out the power:
For any value 
Example Question #12 : Logarithms
Solve for
Round to the nearest hundredth.
To solve an exponential equation like this, you need to use logarithms. This can be translated into:
Now, remember that your calculator needs to have this translated. The logarithm 
Remember that you have the equation:
Thus, 
Example Question #13 : Logarithms
Solve the following equation
In order to solve a question like this, you will need to use logarithms. First, start by converting this into a basic logarithm:
Recall that you need to convert 
Thus, you can solve for 
Example Question #14 : Logarithms
At the end of each year, an account compounds interest at a rate of 
The general function that defines this compounding interest is:
What we are looking for is:
You can solve this using a logarithm. First, isolate the variable term by dividing both sides:
Which is:
Next, recall that this is the logarithm:
For this, you will need to do a base conversion:
This is
This means that it will take 
Example Question #11 : Logarithms
What is the value of 
Remember that you will need to calculate your logarithm by doing a base conversion. This is done by changing 
Using your calculator, you can find this to be:
Example Question #16 : Logarithms
if 
The first step of this problem is to find
y is found to be 2. The next step is to plug y in to the second log.
Example Question #17 : Logarithms
Find 
expands to
expands to
Example Question #18 : Logarithms
Simplify:
Here, we need to make use of some logarithm identities: 
Therefore, putting all of those things together, we get the final answer of
Example Question #19 : Logarithms
If
then what is 
This is a test of translating logarithmic/exponential properties, with the key here being to realize that
With that in mind, here is how it works out:
Hence, 
Example Question #20 : Logarithms
A.
B.
C.
A only
A, B and C
B only
B and C only
A and B only
A, B and C
A is true in two ways. You can use the fact that if a logarithm has no base, you can use base 10, or you can use the fact that you can use this property:
B is a simple change of base application, and C is simply computing the logarithm.
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