Precalculus Logarithmic and Exponential Function Review

When solving an exponential function with different bases:

• you take the ln or log of each term, follow logarithmic rules, then rearrange to get x by itself

• you can only take the ln of each term

• you can only take the log of each term

You can cancel out the base (e) function be taking the (ln) of each term.

• True

• False

Taking the log of 1 (regardless of the base), always equals 0.

• True

• False

Solve for x

• x = ln 4

• 

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e

Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

Rewrite log_vn = a in exponential form.

• v^a = n

• n^a = v

• vⁿ = a

• aⁿ = v

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

Which of the following is an exponential decay model?

• y = 3 * (1/2)^x

• y = 1/2 * (3)^x

• y = -2 * (2)^x

• y = -3 * (3/2)^x

• x = 2

• x = -2

• y = 2

• y = -2