Math Ladder

Solving logarithmic equations with the definition worksheets Grade 11

Rewrite a logarithm in exponential form, then solve.

The front of the free solving logarithmic equations with the definition worksheet

Free · Worked example · 26 problems · Answer key · US Letter

UnlimitedFresh versions and 5-sheet packetsGet Unlimited →

How to do it

log base b of y = n means bⁿ = y. Rewrite, then solve.

log⁡2(2x−12)=2x=8\log_{2} (2x - 12) = 2\quad x = 8
2x−12=42x - 12 = 4rewrite: 2² = 4
2x=162x = 16
x=8x = 8divide by 2

Example problems

  1. log⁡5(2x−29)=1\log_{5} (2x - 29) = 1
  2. log⁡2x=3\log_{2} x = 3
  3. log⁡5(x+131)=3\log_{5} (x + 131) = 3
  4. log⁡4x=4\log_{4} x = 4

Exponential and logarithmic functions

  1. Solving exponential equations with a common base
  2. Evaluating logarithms
  3. Solving logarithmic equations with the definition
  4. Logarithm rules with numbers
  5. Expanding and condensing logarithms
  6. Change of base formula
  7. Solving exponential equations with logarithms
  8. Solving logarithmic equations
  9. Exponential growth and decay