Solving Exponential Equations
Determine the Value of X that makes the equation true (or satisfies the equation)
8 x - 2 = 2 x + 4
Solution 1 guess and check
Sub in different values of x, trying to get closer and closer.
Not a very efficient way of solving equations.
Solution 2 equating the bases
If an equation can be re-arranged so that the bases are the same, this means the exponents than have to be equivalent as a result.
In this case we can re-write 8 with a base of 2 and an exponent of 3. Using exponent laws we see that:
Â· Get the bases to be the same
Â· Factor out a common factor (involving an exponent)
Â· Note knowing the powers of 2 from 0 to 10 is very helpful, same with the powers of 3 from 1 to 5.
Â· Reduce the expression to only two parts (one with an unknown exponent and a constant term)
o Common methods Factoring, BEDMAS rules, Exponent laws
Â· Find a common base
o NOTE zero can be an base with an exponent zero.