# Write as sum difference or multiple of logarithms worksheet

### Properties of logarithms worksheet answers

Also, we can only deal with exponents if the term as a whole is raised to the exponent. In addition, the presence of a square root on the numerator adds some level of difficulty. Since we have the difference of logs, we will utilize the Quotient Rule. Practice with Worksheets. No big deal then. Substitute back into the original logarithmic equation and verify if it yields a true statement. It looks like we are dealing with a quadratic equation. What we want is to have a single log expression on each side of the equation.

I used different colors here to show where they go after rewriting in exponential form. Given I color coded the parts of the logarithmic equation to show where they go when converted into exponential form.

Factor out the trinomial.

## Write the expression as a sum or difference of logarithms calculator

Given Move all the logarithmic expressions to the left of the equation, and the constant to the right. It looks like this after getting its Cross Product. Either of the two answers should be correct. The expression inside the parenthesis stays in its current location while the constant 3 becomes the exponent of the log base 3. Remember that a radical can be expressed as a fractional exponent. To solve this Rational Equation, apply the Cross Product. Descriptions of Logarithm Rules The logarithm of the product of numbers is the sum of logarithms of individual numbers. Apply the Quotient Rule since they are the difference of logs.

Here is the answer for this part. Note that all of the properties given to this point are valid for both the common and natural logarithms.

This means that we can use Property 5 in reverse. This will use Property 7 in reverse. Bring down that exponent 4 using Power Rule.

In fact, logarithm with base 10 is known as the common logarithm. Practice with Worksheets.

## Write the expression as a sum and or difference of logarithms with all variables to the first degree

I used different colors here to show where they go after rewriting in exponential form. Check your potential answer back into the original equation. We will have expressions that look like the right side of the property and use the property to write it so it looks like the left side of the property. Also, this is the first time we see Rule 5 or Identity Rule of Logarithm in action. To solve this Rational Equation, apply the Cross Product. Then further condense the log expressions using the Quotient Rule to deal with the difference of logs. Therefore, exclude it as part of your solution.

This is where we say that the stuff inside the left parenthesis equals the stuff inside the right parenthesis.

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