Teaching Notes 8.16: Solving Exponential Equations
Solving exponential equations requires students to express each side of the equation as a power
of the same base. Sometimes students forget to write both sides of the equation as two
expressions that have the same base or they write an incorrect equation.- Explain that an exponential equation is an equation that has a variable in the exponent. For
example, 9^2 = 3 xand 2^3 x= 2 x−^1. Note that the variable in the exponent may be on only one
side or both sides of the equation. - Explain that if the two bases are the same, then the equation must be true if the exponents
have the same value. Students can then write an equation stating that the two exponents are
equal and then solve the equation. - Explain that if the bases are different, students must rewrite the equation so that the bases
are the same. Depending on the abilities of your students, you may wish to review some of
the more common powers, for example, 2^2 =4, 2^3 =8, 4^2 =16, 5^3 =125, and so on. - Review the information and examples on theworksheet with your students. Note that in the
first example, students do not have to rewrite the equation because the common base is 2. In
the second example, 9^2 is expressed as (3^2 )^2 or 3^4. The equation in the second example could
also have been rewritten as 9^2 =(9
1(^2) )x. Remind your students that when they find powers of
powers, they should multiply the exponents.
EXTRA HELP:
This method may be used only when one base is raised to a power on each side of the equation.
ANSWER KEY:
(1)x=− 1 (2)x= 3 (3)x= 1 (4)x=
3
2
(5)x= 0 (6)x= 5
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(Challenge)Both are correct. The bases in the equation must be the same. In this case, 9 or 3
may be used as the base.
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