# Rewrite as sum or difference of logarithms

Example 5 Write each of the following as a single logarithm with a coefficient of 1. The second logarithm is as simplified as we can make it. Also, we can only deal with exponents if the term as a whole is raised to the exponent.

I can put together that variable x and constant 2 inside a single parenthesis using division operation.

Again, note the use of parentheses. In these cases it is almost always best to deal with the quotient before dealing with the product. Rule 6: Log of Exponent Rule The logarithm of an exponential number where its base is the same as the base of the log equals the exponent.

Just a reminder, you add the exponents during multiplication and subtract during division.

### Logarithm calculator

First, we'll replace the radical with a fractional exponent: Now we'll use the first property to move the exponent out in front: Next we'll use the third property to rewrite the logarithm of the fraction as a difference of logarithms. Practice with Worksheets. This will use Property 7 in reverse. In order to use Property 7 the whole term in the logarithm needs to be raised to the power. We have to rewrite 3 in logarithmic form such that it has a base of 4. If this is not your problem, please repost the problem with parentheses around: Radicands expressions within radicals Denominators Exponents I'm not sure when "product of logarithms" would ever arise but I think I know what the problem is asking. Rule 7: Exponent of Log Rule Raising the logarithm of a number by its base equals the number.

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