Solve an Exponential Equation Using Logarithms

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₈₁3 = 4

• log₃81 = 4

• log₄81 = 3

2⁵ = 32

• log ₅ 32 = 2

• log ₂ 32 = 5

• log ₃₂ 5 = 2

• log ₂ 5 = 32

Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

log₂(x+3)=4

• 16

• 13

• 3

• 10

Ms. Jones isn't sure if she solved this logarithmic equation correctly. Check her work to determine if she made any mistakes. If she did make a mistake, determine what it was.

• She did not convert to exponential form correctly.

• She did not distribute the 4 when combining the logs.

• She should have subtracted 2 from both sides instead of adding 2.

• No mistakes were made!

Mrs. Cruise isn't sure if she solved this logarithmic equation correctly. Check her work to determine if she made any mistakes. If she did make a mistake, determine what it was.

• She did not convert to exponential form correctly.

• She should have divided the arguments.

• She used the incorrect base when converting to exponential form.

• No mistakes were made!