# How To Solve Problems With Exponents

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.

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

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$\,\,\,\, = \,\,\,x = y$ Note that this fact does require that the base in both exponentials to be the same. $\begin3x & = 7x - 2\\ 2 & = 4x\\ \frac & = x\end$ So, if we were to plug $$x = \frac$$ into the equation then we would get the same number on both sides of the equal sign.

Again, there really isn’t much to do here other than set the exponents equal since the base is the same in both exponentials.

$\frac =$ 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.

The reality is that we can use any logarithm to do this so we should pick one that we can deal with.

This usually means that we’ll work with the common logarithm or the natural logarithm.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.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.So, let’s work a set of examples to see how we actually use this idea to solve these equations.Okay, so we say above that if we had a logarithm in front the left side we could get the $$x$$ out of the exponent. We’ll just put a logarithm in front of the left side.You will be able to solve these, as long as you correctly utilize the properties of exponents and apply the properties of algebraic equations that you have been using in your class all along. Her biomedical engineering research, "Biocompatible and p H sensitive PLGA encapsulated Mn O nanocrystals for molecular and cellular MRI," was accepted in 2010 for publication in the journal "Nanoletters." Lobo earned her Bachelor of Science in biomedical engineering, with distinction, from Yale in 2010. Due to the nature of the mathematics on this site it is best views in landscape mode.That is not the problem that it might appear to be however, so for a second let’s ignore that.The real issue here is that we can’t write 8 as a power of 4 and we can’t write 4 as a power of 8 as we did in the previous part.

## Comments How To Solve Problems With Exponents

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