SOLVING EXPONENTIAL EQUATIONS
Two exponential expressions with the same base are equal when their
exponents are equal.
If am = an, then m = n, where a > 0, a  1, and m, n  R.
If two expressions are equal, then taking the logarithm of both expressions
maintains their equality.
If M = N, then logaM = logaN, where a > 0, a  1, and M, N > 0.
Example 
Solve, rounding to 2 decimal places where necessary:
a)
42x = 25–x
b)
2x = 7
c)
3x+1 + 3x = 324
d)
2x+1 = 3x–1
Summary
A
To solve an exponential equation algebraically:



write both sides of the equation with the same base
set exponents equal to each other
solve for the unknown
OR
B
Example 



take the log of both sides of the equation using base 10
use the power rule for logs to simplify the equation
solve for the unknown
The half-life of radioactive radon is 4 days. Determine how long
it will take 200g of radon to be reduced to 12.5g.
t
 1 h
M(t)  P 
2
Homework: p.485–486 #1cdf, 2bcf, 3ace, 4a, 5, 7,
8ace, 10bc, 12, 14, 17ac