### All Algebra II Resources

## Example Questions

### Example Question #1 : Logarithms And Exponents

**Possible Answers:**

**Correct answer:**

is equivalent to . In other words, we know the base and we know the result; we're looking for the exponent to get us there.

The best way to solve a problem like this is to use a base change. can also be solved as . The great part of this is that when you use the function on your calculator, it's already set to a base of .

Go ahead and plug in the numbers from the problem to solve.

### Example Question #2 : Logarithms And Exponents

Which equation is equivalent to:

**Possible Answers:**

**Correct answer:**

,

So,

### Example Question #3 : Logarithms And Exponents

What is the inverse of the log function?

**Possible Answers:**

**Correct answer:**

This is a general formula that you should memorize. The inverse of is . You can use this formula to change an equation from a log function to an exponential function.

### Example Question #4 : Logarithms And Exponents

Solve for :

Round to the nearest hundredth.

**Possible Answers:**

Cannot be computed

**Correct answer:**

To solve this, you need to set up a logarithm. Our exponent is . The logarithm's base is . The value is the operand of the logarithm. Therefore, we can write an equation:

Now, you cannot do this on your calculator. Therefore, using the rule for converting logarithms, you need to change:

to...

You can put this into your calculator and get:

, or rounded,

### Example Question #5 : Logarithms And Exponents

Solve for :

Round to the nearest hundredth.

**Possible Answers:**

**Correct answer:**

To solve this, you need to set up a logarithm. Our exponent is . The number of which it is the exponent of is the *base*. This is the logarithm's base. The value is the operand of the logarithm. Therefore, we can write an equation:

Now, you cannot do this on your calculator. Therefore, using the rule for converting logarithms, you need to change:

to...

You can put this into your calculator and get:

, or rounded,

### Example Question #6 : Logarithms And Exponents

Solve for :

Round to the nearest hundredth.

**Possible Answers:**

**Correct answer:**

To solve this, you need to set up a logarithm. Our exponent is . The number of which it is the exponent of is the *base*. This is the logarithm's base. The value is the operand of the logarithm. Therefore, we can write an equation:

Now, you cannot do this on your calculator. Therefore, using the rule for converting logarithms, you need to change:

to...

You can put this into your calculator and get:

, or rounded,

### Example Question #7 : Logarithms And Exponents

Solve for :

Round to the nearest hundredth.

**Possible Answers:**

**Correct answer:**

To solve this, you need to set up a logarithm. Our exponent is . The number of which it is the exponent of is the *base*. This is the logarithm's base. The value is the operand of the logarithm. Therefore, we can write an equation:

to...

You can put this into your calculator and get:

, or rounded,

### Example Question #8 : Logarithms And Exponents

Write the equation in logarithmic form.

**Possible Answers:**

**Correct answer:**

For logarithmic equations, can be rewritten as .

In this expression, is the base of the equation (). is the exponent () and is the term ().

In putting each term in its appropriate spot, the exponential equation can be converted to **.**

### Example Question #9 : Logarithms And Exponents

Solve the following logarithm for :

**Possible Answers:**

**Correct answer:**

Solve the following logarithm:

Recall that we can convert logarithms to exponential form via the following:

Using this approach, convert the given log to exponential form:

### Example Question #10 : Logarithms And Exponents

Rewrite the following expression as an exponential expression:

**Possible Answers:**

**Correct answer:**

Rewrite the following expression as an exponential expression:

Recall the following property of logs and exponents:

Can be rewritten in the following form:

So, taking the log we are given;

We can rewrite it in the form:

So b must be a really huge number!

### All Algebra II Resources

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