Rewriting Logarithms Notes

Rewrite 3⁴ = 81 in logarithmic form.

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

Write in exponential form.
log₂(¹/₈) = -3

• 2^-3 = ¹/₈
• 2^1/8 = -3
• -3² = ¹/₈
• -3^1/8 = 2

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Write log₂ 0.25 = -2 in exponential form

• -2²  = 0.25
• -2^0.25  = 2
• 2^-2  = 0.25
• No correct answer

Write  5² = 25  in logarithmic  form

• log₅   2 = 25
• log₅    25  =  2
• log₂  25  = 5
• No Correct Answer

Write in logarithmic form.
2^-4 = ¹/₁₆

• log₂(¹/₁₆) = -4
• log_-4(¹/₁₆) = 2
• log _-4 2 = ¹/₁₆
• log₂(-4) = ¹/₁₆

Natural log has a base of ________.

• π
• μ
• θ
• e

Rewrite log₃t = 5 in exponential form.

• 5^t=3
• log₃5 = log₃t
• t⁵=3
• 3⁵=t

Rewrite in exponential form:
log(10,000)=4.

• e⁴=10,000
• 4^10,000=10
• 10⁴=10,000
• 0⁴=10

The common logarithm has what base?

• 10
• 0
• e
• -e