*The first thing to do in this problem is to get the same base on both sides and to so that we’ll have to note that we can write both 4 and 8 as a power of 2. \[\begin & = \frac\ & = \frac\end\] It’s now time to take care of the fraction on the right side.To do this we simply need to remember the following exponent property.Recall the following logarithm property from the last section.*

*The first thing to do in this problem is to get the same base on both sides and to so that we’ll have to note that we can write both 4 and 8 as a power of 2. \[\begin & = \frac\ & = \frac\end\] It’s now time to take care of the fraction on the right side.*

The important part of this property is that we can take an exponent and move it into the front of the term.

So, if we had, \[\] we could use this property as follows. Of course, we are now stuck with a logarithm in the problem and not only that but we haven’t specified the base of the logarithm.

In your algebra classes, you will often have to solve equations with exponents.

Sometimes, you may even have double exponents, in which an exponent is raised to another exponential power, as in the expression (x^a)^b.

Now, in this case we don’t have the same base so we can’t just set exponents equal. \[ = \] Now, we still can’t just set exponents equal since the right side now has two exponents.

However, with a little manipulation of the right side we can get the same base on both exponents. If we recall our exponent properties we can fix this however.

One method is fairly simple but requires a very special form of the exponential equation.

The other will work on more complicated exponential equations but can be a little messy at times. This method will use the following fact about exponential functions. 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 \(x\).

\[\frac = \] Using this gives, \[ = \] So, we now have the same base and each base has a single exponent on it so we can set the exponents equal.

\[\begin2\left( \right) & = - 3\left( \right)\ 10 - 18x & = - 3x 6\ 4 & = 15x\ x & = \frac\end\] And there is the answer to this part.

## Comments How To Solve Problems With Exponents

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