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The reverse process of expanding logarithms is called combining or condensing logarithmic expressions into a single quantity. Other textbooks refer to this as simplifying logarithms.

Condensing Logarithmic Expressions - YouTube YouTube Start of suggested clip End of suggested clip So how can we express this expression as a single log the first thing we need to do is move theMoreSo how can we express this expression as a single log the first thing we need to do is move the coefficient to the exponent. Position so this is going to be log a squared plus log b to the fifth.

Logarithms : Expanding and Combining , Example 3 - YouTube YouTube Start of suggested clip End of suggested clip We could write our next term as the natural logarithm of X cubed. Plus five raised to the 13th.MoreWe could write our next term as the natural logarithm of X cubed. Plus five raised to the 13th. Power. And then we would have minus the natural logarithm of X plus one raised to the one-half.

2nd Law of Logs: Subtracting Logs - YouTube YouTube Start of suggested clip End of suggested clip So what we need to remember is we're subtracting so we divide by what's inside the log functions aMoreSo what we need to remember is we're subtracting so we divide by what's inside the log functions a log of 3 and then 20 divided by 2. And that gives us log.

Combining Logarithmic Expressions - YouTube YouTube Start of suggested clip End of suggested clip Right here it's log base B of a product equals log base B of X plus log base B of Y. So we've gotMoreRight here it's log base B of a product equals log base B of X plus log base B of Y. So we've got the sum of logs the bases have to match up the bases have to match up in order for me to combine them.

You take a log of the numerator minus log of the denominator. So log of the one on top - log of theMoreYou take a log of the numerator minus log of the denominator. So log of the one on top - log of the one on the bottom again keeping the same base. And then the power property for logs.

Condensing logarithmic expressions - YouTube YouTube Start of suggested clip End of suggested clip So here i have the the sum of two logarithms with the same base. So i can rewrite that as theMoreSo here i have the the sum of two logarithms with the same base. So i can rewrite that as the product in one logarithm. So that's going to be x cubed y to the fourth.

Logarithms : Expanding and Combining , Example 3 - YouTube YouTube Start of suggested clip End of suggested clip We could write our next term as the natural logarithm of X cubed. Plus five raised to the 13th.MoreWe could write our next term as the natural logarithm of X cubed. Plus five raised to the 13th. Power. And then we would have minus the natural logarithm of X plus one raised to the one-half.

Combining Logarithmic Expressions - YouTube YouTube Start of suggested clip End of suggested clip Right here it's log base B of a product equals log base B of X plus log base B of Y. So we've gotMoreRight here it's log base B of a product equals log base B of X plus log base B of Y. So we've got the sum of logs the bases have to match up the bases have to match up in order for me to combine them.

To solve this type of problem: Step 1: Change the Base to 10. Using the change of base formula, you have.Step 2: Solve for the Numerator and Denominator. Since your calculator is equipped to solve base-10 logarithms explicitly, you can quickly find that log 50 = 1.699 and log 2 = 0.3010. Step 3: Divide to Get the Solution.