Unit 4
MCR 3U1
Lesson 6: Solving Exponential Equations
An equation such as 2  64 is called an exponential equation, since the unknown is the
exponent in the equation. Other exponential equations are:
n
5 x  625
163n  2  2
These equations can be solved by expressing both sides as powers of the same base. We call this
solving by using common bases. We will get a more accurate answer when solving.
Example 1: Solve each of the following equations.
a) 2 x  64
Write 64 as a power of 2.
When the powers are equal and the bases are the same, the exponents
2 x  26
are equal.
x6
Therefore, x = 6
b)
2 x  4  32
c)
9 x 3  81
d)
e)
3  2 x  12
f)
10  3 x  270
g)
h)
2 x  2  2 x  48
i)
5 x  2  5 x 3  2500  0
5x 
1
25
2 x 5  4 x  2