Take out subject in LOG

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Aug 6th, 2022
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How to take out subject in LOG

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in this lesson weamp;#39;re going to talk about evaluating logs using the change of base formula so we know that log base 2 of 16 is equal to 4 because 2 to the fourth power is 16. but letamp;#39;s say if you donamp;#39;t know that hereamp;#39;s how you can use the change of base formula to get the same answer but hereamp;#39;s the formula log base a of b is equal to log of b divided by log of a and the reason why itamp;#39;s called the change of base formula is because you can change the base originally the base is a but you can make it into any new base weamp;#39;ll call it c c could be 5 8 12. as long as these two are the same it doesnamp;#39;t really matter what c is the equation will work so log base 2 of 16 you can type it in your calculator as log 16 divided by log 2. now when you type it in your calculator like this itamp;#39;s automatically going to make it base 10. so regardless of whatever the new base is you will still get the right answer so go ahead and type that

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When the variable is on one side Take the log of both sides. Use the power rule to drop down the exponent. Divide both sides by the appropriate log to isolate the variable. Solve for the variable.
0:22 3:14 You can rewrite that as an exponent. Inside your logarithm. So therefore i can rewrite this as logMoreYou can rewrite that as an exponent. Inside your logarithm. So therefore i can rewrite this as log base 5 of x squared plus 9 cubed equals 6. All right now you can see that this is in logarithmic.
0:29 1:18 So i can just do log of 5. And then to solve for x i got to divide by 2.. So therefore i have x isMoreSo i can just do log of 5. And then to solve for x i got to divide by 2.. So therefore i have x is approximately. Point three five as i rounded my answer.
Turn the variable inside the log into an exponential equation (which is all about the base, of course). For example, to solve log3 x = 4, change it to the exponential equation 34 = x, or 1/81 = x. Keep in mind that because logs dont have negative bases, you throw the negative one out the window and say x = 4 only.
A logarithm is the inverse of an exponent. The equation log x = 100 is another way of writing 10x = 100. This relationship makes it possible to remove logarithms from an equation by raising both sides to the same exponent as the base of the logarithm.
In order to eliminate the log, which has a default base of 10, we will need to raise both sides of the equation as powers using the value of 10.
This can be done by performing inverse operations on the terms that need to be removed so that the variable of interest is isolated. Subtraction cancels out addition, and vice versa, and multiplication cancels out division, and vice versa. Observe that x = y 2 x = y^2 x=y2 simplifies to y = x .

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