1. Solving exponential equations
Adapted from Walch Education

2. Laws of exponents Law General rule Specific example
Multiplication of exponents
b m • b n = b m + n
46 • 43 = 49
Power of exponents
(b m) n = b mn
(bc) n = b nc  n
(4 6 ) 3 = 4 18
(4 • 2) 3 = 4 32  3
Division of exponents
Exponents of zero
b 0 = 1
40 = 1
Negative exponents
and

3. Solving exponential equations
Rewrite the bases as powers of a common base.
Substitute the rewritten bases into the original equation.
Simplify exponents.
Solve for the variable.

4. Practice # 1
Solve 4x = 1024.
Rewrite the base as powers of a common base.
41 = = 256
42 = = 1024
43 = 64
We now know that it is possible to write 1,024 as a power of 4

5. The solution to the equation 4x = 1024 is x = 5
Rewrite the equation so that both sides have a base of 4.
4x = 45
Now solve for x by setting the exponents equal to each other.
x = 5
The solution to the equation 4x = 1024 is x = 5

6. Thanks For Watching
~Dr. Dambreville