## Solving Common Base Exponential Equations

#### Aligned To Common Core Standard:

**High School Algebra** - HSF-LE.A.4

Tips for Solving Common Base Exponential Equations -
There are two types of exponential equations. The first ones are which has the same bases and the ones without the same bases. Exponential equations are that part of algebra that the students find it difficult to solve.
Out of these two, exponential equations with the same bases are the easiest to solve. We do not have to apply a logarithm to solve them. Whereas to solve exponential equations with unlike bases, one has to apply logarithm.
To solve these equations without using a logarithm, you need to follow several rules. Any variable with zero as its exponent is equal to one. This is known as the zero property.
b^{0} = 1
Then there is the negative exponent property. If the variable has a negative integer in its exponent, reciprocating it will change the negative exponent into the positive exponent.
b^{(-n)} = 1/b^{n}. In multiplication, when the bases are the same, the powers can be added. This is the product rule. (b ^{M}) (b^{N})=b^{(M+N)}
In division, when the bases are the same, the powers can be subtracted. This is the quotient rule. b^{M}/b^{N} =b^{(M-N)}
The last one is the power to a power rule. (b^{M})^{N} = b^{(M.N)}. Students learn how to solve very common trig. problems with this series of lessons and worksheets.

### Printable Worksheets And Lessons

- Find the Variable Step-by-Step Lesson- These problems make it easy to combine, but then you will need to factor your way out of it.
- Guided Lesson - This image always makes me think exponential equations. I was dating a skier in college when I was learning this, I think?
- Guided Lesson Explanation - They follow a simple system here, factor and simplify.
- Practice Worksheet - This is a bit overwhelming at first, but you will get the hang of it.
- Matching Worksheet - Match the x to the equations it goes with.