Exponential and Logarithmic Equations Review

Solving Simple Equations

100

Solve for x. 8^x = 16

x = 4/3

200

Solve for x: 2 ln x - ln 4 = 0

x = 2

300

Solve for x. (1/4)^x = 64

x = -3

400

Solve for x to the nearest thousandth: e^x = 2

x = ln 2 (approximately 0.693)

500

Solve for x using inverse property. Log₅ x = 1/2

5^(1/2) = x, approximately 2.236

Exponential Equations

100

Solve. 2^x =4^(x+1)

What is -2?

200

Solve. 4^-3x=4²

What is x=2/3

300

Solve for x. 2^x+2=16

x = 2

400

Solve for x. 4^-3x=64^3-x

No Solution

500

Solve for x. 36^3x+2=6³

x = -1/6

Logarithmic equations

100

Solve for x algebraically. log₂ 32 = 3x

x = 5/3

200

Solve for x algebraically. Log₂ x = log₂ 12

x = 12

300

Solve. log₃ (20)²

x =5.4537

400

Solve. log_{3 √150}

x = 2.2804

500

Solve for x algebraically. Logx-Log3 =2

What is 300?

Base e and Natural Log

100

Write an equivalent exponential or logarithmic equation. ln 50 = x

e^x = 50

200

Solve, round four decimal spaces. e^3x = 8

x = .6931

300

Solve, round four decimal spaces. ln (x+2) = 3

x = 18.0855

400

Write an equivalent exponential or logarithmic equation. ln 6 = 1.7918 

e^{1.7918 = 6}

500

Solve, round four decimal spaces. e^-4x = 5

x = -.4024