6.6 Solving Exponential and
Logarithmic Equations
Rewrite the exponential equations in logarithmic form and the
logarithmic equations in exponential form. Then solve for x and
check your answer.
1. 2x−1 = 5
2. e−2x = 11
3. 33−2x = 4
4. log2 (x + 5) = −1
5. log(3 − x) = 2
6. ln(2x) =
How can you solve exponential and
logarithmic equations?
Work with a partner. Match each equation with the graph of its related
system of equations. Explain your reasoning. Then use the graph to
solve the equation.
a. ex = 2
b. ln x = −1
c. 2x = 3−x
d. log4 x = 1
e. log5 x =
f. 4x = 2
Solving Exponential Equations
No calculator
Strategy:
Solve.
a.
b.
c.
d.
Calculator
Strategy:
Solve.
e. 2x = 5
f.
g. 79x = 15
h. 4e−0.3x − 7 = 13
y
Solving Logarithmic Equations
logbm = logbn
Strategy:
Solve.
a. ln(4x − 7) = ln(x + 5)
b. log 2x + log(x − 5) = 2
logbm = x
Strategy:
c. log2(5x − 17) = 3
d. log4(x - 7) = 2
k
Solve the equation.
1. 100x =
2. 2x = 5
3. 79x = 15
4. 4e−0.3x − 7 = 13
Solve the equation. Check for extraneous solutions.
5. ln(7x − 4) = ln(2x + 11)
6. log2(x − 6) = 5
7. log 5x + log(x − 1) = 2
8. log4(x + 12) + log4 x = 3