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6.5
Solving Exponential Equations
Notes
Exponential equations are equations in which ______________________________ occur as exponents.
Property of Equality for Exponential Equations
Words
Two powers with the same positive base b, where b  1, equal if and only if
their exponents are equal.
Numbers
If 2 x  25 , then x  5. If x  5, then 2 x  25.
Algebra
If b  0 and b  1, then b x  b y if and only if x  y.
Solve the equation. Check your solution.
1. 34 x  312
2. 8x  5  820
3. 64 x  5  62 x
4. 56 x  3  5 3  4 x
To solve some exponential equations, you must first rewrite each side of the equation using the same
base.
5. 42 x11  1024
6. 83  2 x  512
7. 47  x  256
8. 49 x  2  343
190 Algebra 1
Student Journal
9. 366 x 1  65 x
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10. 9 x  4  813 x
11. 64 x 1  512 x
12. 62 x  362 x 1
*Sometimes, it is impossible to rewrite each side of an exponential equation using the same base. You can
solve these types of equations by graphing each side and finding the points(s) of intersection.
Exponential equations can have no solution, one solution, or more than one solution depending on the
number of points of intersection. * Graphing Calculator*
13.You deposit $1000 in a savings account that earns 5% annual interest compounded yearly.
a. Write an exponential equation to determine when the balance of the account will be $1500.
b. Solve the equation.
Homework #6:
Chapter 6.5
Pg. 329
1,2, 3-11 odd, 19, 43,
50, 60-63
*YOU MUST HAVE
COMPLETE
SENTENCES FOR #1
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Algebra 1
Student Journal
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