# Precalculus : Express Logarithms in Condensed Form

## Example Questions

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### Example Question #1 : Express Logarithms In Condensed Form

Explanation:

You need to know the Laws of Logarithms in order to solve this problem. The ones specifically used in this problem are the following:

Let's take this one variable at a time starting with expanding z:

Now y:

And finally expand x:

### Example Question #92 : Exponential And Logarithmic Functions

What is  equivalent to?

Explanation:

Using the properties of logarithms,

the expression can be rewritten as

which simplifies to .

### Example Question #1 : Express Logarithms In Condensed Form

Find the value of the sum of logarithms by condensing the expression.

Undefined

Explanation:

By the property of the sum of logarithms,

.

### Example Question #2 : Express Logarithms In Condensed Form

Condense the following logarithmic equation:

Explanation:

We start condensing our expression using the following property, which allows us to express the coefficients of two of our terms as exponents:

Our next step is to use the following property to combine our first three terms:

Finally, we can use the following property regarding subtraction of logarithms to obtain the condensed expression:

### Example Question #3 : Express Logarithms In Condensed Form

What is another way of writing

?

Explanation:

Properties of logarithms allow us to rewrite  and  as  and , respectively. So we have

Again, we use the logarithm property

to get

### Example Question #4 : Express Logarithms In Condensed Form

Write the expression in the most condensed form:

Explanation:

Use the Power property of Logarithms:

Rewrite the fractional exponent:

Condense into a fraction using the Quotient property of Logarithms:

### Example Question #97 : Exponential And Logarithmic Functions

Simplify:

Explanation:

When logs of the same bases are subtracted, the contents of both logs will be divided with each other.  When logs of the same bases are added, then the contents inside the log will be multiplied together.

### Example Question #5 : Express Logarithms In Condensed Form

Completely condense the logarithm: .

Explanation:

Apply the Power property:

Apply the quotient property:

### Example Question #99 : Exponential And Logarithmic Functions

Simplify

Explanation:

By the property of the addition of logarithms with the same base

As such

### Example Question #5 : Express Logarithms In Condensed Form

Condense the following equation:

Cannot simplify

Explanation:

Let's use the properties of logarithms to condense this equation.  We will use the follwing three properties

Power Rule

Product Rule

Quotient Rule

Let's first use the power rule to rewrite the second term

Then, we'll use the product rule to combine the first threeterms

Lastly, we'll use the quotient rule to combine into one term

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