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Expanding logarithmic expressions with a square root - YouTube YouTube Start of suggested clip End of suggested clip If i want to expand this logarithm expression the first thing i'm going to want to do is get rid ofMoreIf i want to expand this logarithm expression the first thing i'm going to want to do is get rid of the root. So i can rewrite. This as ln of z. Over z squared plus 1 raised to the one-half.

How to Expand a Logarithm : Logarithms , Lesson 10 - YouTube YouTube Start of suggested clip End of suggested clip So let's go ahead and write that out here so log base 3 of all this stuff is equal to log base 3 ofMoreSo let's go ahead and write that out here so log base 3 of all this stuff is equal to log base 3 of the numerator. So our numerators was on top x squared + y to the 3rd n.

Expanding and Condensing Logs - YouTube YouTube Start of suggested clip End of suggested clip 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.

To expand logarithms, write them as a sum or difference of logarithms where the power rule is applied if necessary. Often, using the rules in the order quotient rule, product rule, and then power rule will be helpful. To simplify logarithms, write them as a single logarithm.

Learn how to expand a logarithmic expression with a square root YouTube Start of suggested clip End of suggested clip Power. So therefore z square root of z is the same thing as z to the one half power. So now byMorePower. So therefore z square root of z is the same thing as z to the one half power. So now by separating this now i have this long exponential logarithm with all these powers.

Step 1: Rewrite the square root as an exponent of 12 . Step 2: Use the power property of logarithms to rewrite the logarithm without the 12 power. Step 3: Use the product and quotient properties of logarithms, if needed, to expand the logarithm.

Expanding logarithmic expressions - YouTube YouTube Start of suggested clip End of suggested clip Minus the ln of y to the fourth. Now my last step is i can take my powers. And i can rewrite them asMoreMinus the ln of y to the fourth. Now my last step is i can take my powers. And i can rewrite them as the product of my logarithm. So therefore i have ln of 6 plus 2 ln of x. Minus 4 ln of y.

Expanding and Condensing Logs - YouTube YouTube Start of suggested clip End of suggested clip So now when you go from the left to the right. That's expanding when you go from the right to theMoreSo now when you go from the left to the right. That's expanding when you go from the right to the left that's condensing you're condensing into just one log. So let's take a look at some examples.

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.

Expanding Logarithmic Expressions - YouTube YouTube Start of suggested clip End of suggested clip Let's try one more example go ahead and expand the log let's say if it's the square root of a timesMoreLet's try one more example go ahead and expand the log let's say if it's the square root of a times b to the one fourth. Divided by the cube root of c to the fifth. Raised to the third.