This page provides a list of educational videos related to Laws of Logarithms. You can also use this page to find sample questions, apps, worksheets, lessons , infographics and presentations related to Laws of Logarithms.

06 - Proving the Logarithm (Log) Rules - Understand Logarithm Rules & Laws of Logs

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18 - Properties of Logarithms (Log x) - Part 1 - Laws of Logs - Calculate Logs & Simplify

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Solving Natural Logarithms | MathHelp.com

In this example, we’re asked to expand the given logarithmic expression, log base 3 of M squared N to the 5th. Remember that our first law of logarithms states that if two values are multiplied together inside a logarithm, such as M squared times N to the 5th, then we can expand the logarithm into the sum of two separate logarithms, in this case log base 3 of M squared plus log base 3 of N to the 5th. Next, notice that each logarithm has a power inside the logarithm, and remember that our third law of logarithms states that if we have a power inside a logarithm, we can move the exponent to the front of the logarithm, so we have 2 times log base 3 of M + 5 times log base 3 of N.

Logarithm Rules: Expanding Logarithms | MathHelp.com

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To simplify 81 to the ½, remember from our study of rational exponents that an exponent of ½ means that we take the square root of the base. In other words, 81 to the ½ means the same thing as the square root of 81. And the square root of 81 is 9. So 81 to the ½ is 9

16 - Simplify Logarithms - Part 1 (Log Bases, Calculate Logarithms & More)

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04 - Solving Logarithmic Equations - Part 1 - Equations with Log(x)

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Evaluating Logarithms | MathHelp.com

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In this example, notice that we have a polynomial divided by a binomial, and our binomial is in the form of an x term minus a constant term, or x – c. In this situation, instead of having to use long division, like we did in the previous lesson, we can divide the polynomials using synthetic division, which is a much more efficient method. Here’s how it works. We start by finding the value of c. Since –c = -3, we know that c = 3. Next, we put the value of c inside a box, so we put the 3 inside a box. It’s very important to understand that the number that goes inside the box always uses the opposite sign as the constant term in the binomial. In other words, since the constant term in the binomial is -3, the number that goes inside the box, is positive 3. Next, we write the coefficients of the dividend, which are 2, -7, 4, and 5. Be very careful with your signs. Now, we’re ready to start our synthetic division. First, we bring down the 2. Next, we multiply the 3 in the box times 2 to get 6, and we put the 6 under the -7. Next, we add -7 + 6 to get -1. Next, we multiply the 3 in the box times -1 to get -3, and we put the -3 under the 4. Next, we add 4 + -3 to get 1. Next, we multiply the 3 in the box times 1 to get 3, and we put the 3 under the 5. Finally, we add 5 + 3 to get 8. Now, notice that we have a 2, -1, 1, and 8 in the bottom row of our synthetic division. These values will give us our answer: the first 3 numbers represent the coefficients of the quotient, and the last number is the remainder. And it’s important to understand that our answer will be one degree less than the dividend. In other words, since our dividend starts with x cubed, and we’re dividing by x, our answer will start with x squared. So our answer is 2x squared – 1x + 1 + 8 over x – 3. Notice that we always use descending order of powers in our quotient. In this case x squared, x, and the constant. Finally, remember that we add the remainder over the divisor, just like we did in the previous lesson on long division, and we have our answer. It’s important to understand that we’ll get the same answer whether we use synthetic division or long division. However, synthetic division is much faster.