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If the exponential equation has the form ab^x=c, first take the log of some sides and past bring down some exponents.
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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.
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.
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.
Is it possible to set exponents equal to 9?
To do this all we need to notice is that 9 = 3 2 9 = 3 2. Here’s what we get when we use this fact. Now, we still can’t just set exponents equal since the right side now has two exponents. If we recall our exponent properties we can fix this however.
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