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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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.

 X LS RS LS = RS 1 1/8 32 NO 2 1 64 NO 5 512 512 YES

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:

 8 x - 2 = 2 x + 4 ( 2 3 ) x - 2 = 2 x + 4 2 3x - 6 = 2 x + 4 3x - 6 = x + 4 2x = 10 x = 5

Other methods:

Â· Get the bases to be the same

Â· Factor out a common factor (involving an exponent)

 3 x + 2 - 3 x = 216 3 x ( 3 2 - 1) = 216 3 x ( 9 - 1) = 216 find a common factor by remembering your exponent laws (am an = am+n ) and then follow BEDMAS rules. Then find a common base and solve for x. 3 x 3 x = 27 3 x = 3 3 x = 3

Â· Note knowing the powers of 2 from 0 to 10 is very helpful, same with the powers of 3 from 1 to 5.

REMEMBER

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.