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Rule 1: xa ∗ xb = xa+b x a ∗ x b = x a + b.
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Solving exponential equations with logarithms worksheet answers
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In this deterrent example we see how to use cardinal of the alkaline logarithm laws to solve exponential equations.
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Do you have to have a coefficient on the exponential?
In order to take the logarithm of both sides we need to have the exponential on one side by itself. Doing this gives, Next, we’ve got to get a coefficient of 1 on the exponential. We can only use the facts to simplify this if there isn’t a coefficient on the exponential.
Which is an example of solving an exponential equation?
Example 1 Solve each of the following. In this first part we have the same base on both exponentials so there really isn’t much to do other than to set the two exponents equal to each other and solve for x x. So, if we were to plug x = 1 2 x = 1 2 into the equation then we would get the same number on both sides of the equal sign.
Why is the X X in the exponent?
The problem here is that the x x is in the exponent. Because of that all our knowledge about solving equations won’t do us any good. We need a way to get the x x out of the exponent and luckily for us we have a way to do that. Recall the following logarithm property from the last section.
How do you move exponents in exponential equations?
Next, in order to move the exponent down it has to be on the whole term inside the logarithm and that just won’t be the case with this equation in its present form. So, the first step is to move on of the terms to the other side of the equal sign, then we will take the logarithm of both sides using the natural logarithm.
Last Update: Oct 2021
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