Combine equation log easily

Aug 6th, 2022
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How to combine equation log

5 out of 5
33 votes

in this question will be combining this log expression into just one single log ok so here is the things that we have to do first look at the number in front of the locks if theres any numbers bring them to the exponent the first one is good right because well just half a one right here technically but a second one is not that good because we have the one half x its ok its just an easy fix Im just going to bring this to the exponent right here likewise for the third one we also have the five dont worry about the minus just look at the five i will look at the phi and bring them to the exponent like that ok and then we will have this is log X plus the one half will be right here so therefore we have log of Y to the one-half power and then minus ok Im maintained de- all I want to do right now is put a file for the exponent of Z so we will have log of Z to the fifth power like that and now we are ready to go to combine to just one single law and this is how you should do it you know

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ln(x)(y) = ln(x) + ln(y) ln(x)(y) = ln(x) + ln(y) The natural log of the multiplication of x and y is the sum of the ln of x and ln of y. Example: ln(8)(6) = ln(8) + ln(6)
To rid an equation of logarithms, raise both sides to the same exponent as the base of the logarithms.
Step 1: Use logarithm properties to rewrite the logarithms so that each side of the equation contains exactly one logarithm with the same base. Step 2: Set the arguments (inputs) of the logarithms equal to each other. Step 3: Solve for the variable. Step 4: Check your solution in the original equation.
Logs of the same base can be added together by multiplying their arguments: log(xy) = log(x) + log(y). They can be subtracted by dividing the arguments: log(x/y) = log(x) - log(y).
0:51 3:07 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.
0:20 1:21 Condensing logarithmic expressions - YouTube YouTube Start of suggested clip End of suggested clip So we have log base 3 of x. Plus log base 3 of y to the fourth thats 3q x cubed. Minus log base 3MoreSo we have log base 3 of x. Plus log base 3 of y to the fourth thats 3q x cubed. Minus log base 3 of z to the fourth.
If you have the same operation on both sides of an equation, they cancel each other out! Keep in mind that this only works when the logarithms on both sides of the equation have the same base. If you had a logarithm with base 3 on one side and a logarithm with base 7 on the other side, they wont cancel out.
You take logarithms on both sides. This is one way to differentiate exponents, when both the base and the exponent depend on the variable (for example, on x).

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