How To Solve Problems With Exponents

In this part we’ve got some issues with both sides.

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Recall the following logarithm property from the last section.

\[ = ra\] Note that to avoid confusion with \(x\)’s we replaced the \(x\) in this property with an \(a\).

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Now that we’ve seen the definitions of exponential and logarithm functions we need to start thinking about how to solve equations involving them.

Now, the equations in the previous set of examples all relied upon the fact that we were able to get the same base on both exponentials, but that just isn’t always possible. \[ = 9\] This is a fairly simple equation however the method we used in the previous examples just won’t work because we don’t know how to write 9 as a power of 7.

In fact, if you think about it that is exactly what this equation is asking us to find.

\[ = \] We now have the same base and a single exponent on each base so we can use the property and set the exponents equal.

Doing this gives, \[\beginz & = 2\left( \right)\ z & = 2z 10\ z & = -10\end\] So, after all that work we get a solution of \(z= -10\) .

In this section we will look at solving exponential equations and we will look at solving logarithm equations in the next section.

There are two methods for solving exponential equations.


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