All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Evaluating Logarithms
Solve:
Step 1: Re-write the log equation as an exponential equation. To do this, take the base of the log function and raise it to the number on the right side of the equal sign. This new exponent is equal to the number to the right of the log base.
Step 2: Re-write the right hand side as a power of 4..
Step 3: Re-write the equation
Step 4: We have the same base, so we can equal the exponents..
Example Question #1 : Evaluating Logarithms
In order to solve for x, we must first rewrite the log in exponential form.
Every log is written in the below general form:
In this case we have:
This becomes:
We can solve this by taking the square root of both sides:
Example Question #1 : Logarithms
Solve for :
Use rules of logarithms...
Take the base of the log and raise it to the number on the right side of the equal sign (which becomes the exponent):
Example Question #1 : Evaluating Logarithms
Evaluate:
Step 1: Write the expression in exponential form...
Given:
Step 2: Convert the right hand side into a power of 6..
Step 3: Re-write the equations...
Since the bases are equal, taking log of both sides will cancel them.
Example Question #1 : Logarithms
Example Question #1 : Logarithmic Properties
Rewrite the following expression as a single logarithm
Recall a few properties of logarithms:
1.When adding logarithms of like base, we multiply the inside.
2.When subtracting logarithms of like base, we divide the inside.
3. When multiplying a logarithm by a number, we can raise the inside to that power.
So we begin with this:
I would start with 3 to simplify the first log.
Next, use rule 1 on the first two logs.
Then, use rule 2 to combine these two.
So our answer is 6.06.
Example Question #1 : Logarithms
When combining logarithms into one log, we must remember that addition and multiplication are linked and subtraction and division are linked.
In this case we have multiplication and division - so we assume anything that is negative, must be placed in the bottom of the fraction.
Example Question #1 : Logarithmic Properties
When rewriting an exponential function as a log, we must follow the model below:
A log is used to find an exponent. The above corresponds to the exponential form below:
Example Question #1 : Logarithms
In order to rewrite a log, we must remember the pattern that they follow below:
In this question we have:
Example Question #1 : Logarithms
Express as a single logarithm.
Step 1: Recall all logarithm rules:
Step 2: Rewrite the first term in the expression..
Step 3: Re-write the third term in the expression..
Step 4: Add up the positive terms...
Step 5: Subtract the answer the other term from the answer in Step 4.
All GRE Subject Test: Math Resources
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