Review: Rewriting Exponential & Logarithmic Functions (10 n & e)

The common logarithm has what base?

• 10
• 0
• e
• -e

Reorder the steps to change an exponential function to a logarithmic function.

• Isolate the exponential function (if necessary)

• Enlarge/

  expand the exponent

• Move the base to the other side of the equal sign and left of the value

• Change log base e to ln

  (if necessary)

• Add log to the left of the base

Reorder the steps to change a logarithmic function to an exponential function.

• Remove log from the left of the base

• Change ln to log base e

  (if necessary)

• Move the base to the other side of the equal sign below the exponent

• Shrink/move up

  the exponent

Write 10⁴= 10000 in logarithmic form.

• log₁₀ 4 = 10000
• log₁₀₀₀₀ 4 = 10
• log₁₀ 10000 = 4
• log₄ 10000 = 10

Write in logarithmic form:
9² = 81

• log ₉ 81 = 2
• log ₂ 81 = 9
• log ₉ 2 = 81
• log ₂ 9 = 81

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Convert 6^(x+2)=216 to logarithmic form

• log₂₁₆(x+2)=6
• log₆(x+2)=216
• log₆(216)=x+2
• log_(x+2)(216)=6