SM 10.6 Logarithms

Change to Logarithmic Form:
12² = 144

• log ₂ 144 = 12
• log ₁₂ 144 = 2
• log ₁₂ 2 = 144
• log ₂ 12 = 144

True or False: log₈64=2

• True
• False

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3
• 2³ = 8
• 3² = 8
• 8³ = 2

Change to Exponential Form:
log₃ 81 = 4

• 81³ = 4
• 81⁴ = 3
• 3⁴ = 81
• 4³ =81

Change to Logarithmic Form:
5³ = 125

• log ₅ 125 = 3
• log ₃ 125 = 5
• log ₅ 3 =125
• log₁₂₅ 3 = 5

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Rewrite 3⁴ = 81 in logarithmic form.

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

Rewrite log_vn = a in exponential form.

• v^a = n
• n^a = v
• vⁿ = a
• aⁿ = v

Change to Exponential Form:
log₂₈₉ 17 = 1/2

• 289^1/2 = 17
• 17^1/2 = 289
• 289¹⁷ = 1/2
• 1/2¹⁷ = 289

Rewrite log_x95 = 2.3

• x^2.3 = 95

• 95^2.3 = x

• 2.3⁹⁵ = x

• x⁹⁵ = 2.3