How do we solve exponential equations?

How do we solve exponential equations?

Exponential equations is another fancy way of say equations with different types of exponents. From positive to negative exponents, from whole numbers to fractions, variables to non-variables. 

You get the point !

SO to start of with the basics let's introduce the exponents. There are normal positive exponents, which everyone can do (on a calculator of course).

2⁴ = 16

Then there's negative exponents, where the outcome is basically a fraction form. For example if you have 2 to the -4. It's basically the same as 1 divided by 2⁴.

Therefore 2⁴ is equal to 16, so your answer would be   1  

                                                                                       16

Next there's fractioned exponents, where you'd probably get 2 to the 1/4. Here's a trick to that ! When you get 1/2 as an exponent, that's basically the same as square rooting the number you have. 

So if you get any number bigger than 2 as the denominator of the fraction (in the exponent), that would go outside the square root. 

 

Last but not least there are exponents with variables. You'll get a problem that looks like this:

2^x+4 = 8

First you have to make both bases equal, so you'd turn 8 into 2³.

2^x+4 = 2³

Then you take exponents and re-write it as an equation to find x.

x+4 = 3

(x = -1)

To make sure that the answer works you need to plug it back in and see if the equation is correct. When you get problems that have 2 answers, you'll need to plug it back in more often to se if one of the answer don't work. 

Sources:

1. John Schnatterly: johnschnatterly.blogspot.com
2. http://www.purplemath.com/modules/solvexpo2.htm
3. http://www.mathsisfun.com/algebra/exponent-fractional.html