Precalculus Logarithmic and Exponential Function Review

Rewrite log_pt = m in exponential form.

• p^t = m

• t^m = p

• m^t = p

• p^m = t

log₅25 = ?

• 2

• 5

• 125

• 10

Use multiple log properties to write as a single log:
3log₂x -  log₂y + log₂z

• log₂(x/(yz))

• log₂(x³yz)

• log₂(x³z/y)

• log₂(x³/(yz))

Expand completely: log(2x⁵) 

• log 2 + 5log x

• 5log 2 + 5log x

• 5log 2 + log x

• log 10 + log x

Is this exponential growth or decay?

• Growth

• Decay

Evaluate log₈ 8

• 8

• -1

• 0

• 1

Find the domain and range of:
f(x) = log₂(x)

• D: all real numbers
  R: y > 0

• Domain: all real numbers
  Range: all real numbers

• Domain: x > 0
  Range: all real numbers

• Domain: all real numbers
  Range: y < 0

Expand:

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• 
• 
• 

Solve for x:

2(3)^x+1 = 36

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Using the parent function y=3^x what would the graph of y=3^x+1 look like?

• Horizontal shift left one unit

• Horizontal shift right one unit

• Vertical shift up one unit

• Vertical shift down one unit