# Write as sum difference or multiple of logarithms definition

### Express the following as a sum difference or multiple of logarithms

The denominator of the quotient will be the natural log with argument 5. And frankly, this is already quite simple. We rewrite the log as a quotient using the change-of-base formula. So b to the zth power is equal to c. In this direction, Property 7 says that we can move the coefficient of a logarithm up to become a power on the term inside the logarithm. This is a nice fact to remember on occasion. And so the logarithm property it seems like they want us to use is log base-- let me write it-- log base b of a times c-- I'll write it this way-- log base b of a times c. So this is just an alternate way of writing this original statement, log base 3 of 27x. The numerator of the quotient will be the natural log with argument 3. We know that already-- times b to the z power.

Note that all of the properties given to this point are valid for both the common and natural logarithms. The denominator of the quotient will be the natural log with argument 5.

## Sum and difference of logarithms calculator

Now, this right over here is telling us that b to the y power is equal to a. Now, what we know is, this thing right over here or this thing right over here tells us that b to the x power is equal to a times c. So this right over here evaluates to 3. And then this right over here, we can evaluate. We do, however, have a product inside the logarithm so we can use Property 5 on this logarithm. Measurements of pH can help scientists, farmers, doctors, and engineers solve problems and identify sources of problems. But let's give our best shot at it. This is the same statement or the same truth said in a different way. Show Solution The pH increases by about 0. You just have to realize that logarithms are really just exponents. This tells us, what power do I have to raise 3 to to get to 27? This will use Property 7 in reverse. I'm writing it as an exponential function or exponential equation, instead of a logarithmic equation. Here is the first step in this part.

We know that already-- times b to the z power. In these cases it is almost always best to deal with the quotient before dealing with the product.

## Power property of logarithms

Show Solution. It follows that the change-of-base formula can be used to rewrite a logarithm with any base as the quotient of common or natural logs. We will use the common log. But let's just apply this property right over here. So this right over here evaluates to 3. But it's even better if you know the intuition. But when we rewrite it, this first term becomes 3. The second logarithm is as simplified as we can make it. Now, this right over here is telling us that b to the y power is equal to a.

So if we apply it to this one, we know that log base 3 of 27 times x-- I'll write it that way-- is equal to log base 3 of 27 plus log base 3 of x.

The numerator of the quotient will be the natural log with argument 3. Measurements of pH can help scientists, farmers, doctors, and engineers solve problems and identify sources of problems.

Here is the answer for this part. We rewrite the log as a quotient using the change-of-base formula. This is the same statement or the same truth said in a different way. Applications of Properties of Logarithms In chemistry, pH is a measure of how acidic or basic a liquid is.

Now, what we know is, this thing right over here or this thing right over here tells us that b to the x power is equal to a times c.

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