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Solving Equations with Exponents Solving Equations with Exponents Now that we’ve seen the definitions of exponential and logarithm functions we need to start thinking about how to solve equations involving them. 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. 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. Let’s start off by looking at the simpler method. This method will use the following fact about exponential functions. Note that this fact does require that the base in both exponentials to be the same. If it isn’t then this fact will do us no good. Suppose there is a number 5 whose exponent is 2 then we can write it as a 52 . In the above example there is a number 5 which represents the value of the base and 2 represents the value of exponent. So, in the general, mean exponents are those values which can be represented as ab, where a refers to the base and b refers to the exponent. These representations of values are called as exponential representations. Example: what is the value of 52 ? Know More About :- Trigonometric Identities

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Solution: in the above question 5 is base and 2 is the exponent, then exponent is the number from which base is multiplied by itself. Let see how. 52 = 5 * 5 = 25 Now we come to the point Order of Operations with Exponents. In this rules of operations are same like normal order of operations but after solving brackets exponents must be solved. Lets see this process by following given example: Example 2 : Solve the expression 35 – (4 * 5)2? Solution: To solve above question we follow the order of operation with exponents: 35 – (4 + 5)2 (In this we first solve the brackets by solving exponent first) 35 – (16 + 25) (Now we solve inner operation of brackets) 35 – 41 -7

(This is our final answer.)

There are various steps related to factoring an equation. The steps are needed to be followed at the time of solving an equation. To solve the problem by factoring process contains the four basic steps. a)

First of all analyze the equation completely.

b) Then move all the given terms in the equation into one side of the equation. Normally these processes are performed by using the addition and subtraction by moving to the left side.\ c)

Now perform the factor of the equation completely. Read More About :- Completing the Square

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Solving Equations with Exponents