# Algebra II : Logarithms and exponents

## Example Questions

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### Example Question #1 : Logarithms And Exponents

Explanation:

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:

Explanation:

So,

### Example Question #3 : Logarithms And Exponents

What is the inverse of the log function?

Explanation:

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.

Cannot be computed

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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 #8 : Logarithms And Exponents

Write the equation  in logarithmic form.

Explanation:

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 :

Explanation:

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:

Explanation:

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!

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