GRE Subject Test: Math : Logarithms

Example Questions

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Example Question #1 : Logarithms

Solve:

Explanation:

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 : Logarithms

Explanation:

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

Explanation:

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 : Logarithms

Evaluate:

Explanation:

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.

Explanation:

Example Question #1 : Logarithmic Properties

Rewrite the following expression as a single logarithm

Explanation:

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:

Next, use rule 1 on the first two logs.

Then, use rule 2 to combine these two.

Example Question #1 : Logarithmic Properties

Explanation:

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 #8 : Logarithms

Explanation:

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 #9 : Logarithms

Explanation:

In order to rewrite a log, we must remember the pattern that they follow below:

In this question we have:

Example Question #2 : Logarithms

Express  as a single logarithm.

Explanation:

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.

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