Log and Exponential Review

Change to exponential form.

log_a2 = 5

• a² = 5

• 5² = a

• a⁵ = 2

• 2⁵ = a

Change to logarithmic form.

3^h = w

• log_w3 = h

• log₃w = h

• log_h3 = w

• log₃h = w

Rewrite log₃t = 5 in exponential form.

• 5^t=3
• log₃5 = log₃t
• t⁵=3
• 3⁵=t

Write in exponential form:

log ₂ 32 = 5

• 2⁵ = 32

• 5² = 32

• 5³² = 2

• 2³² = 5

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

Solve the equation for x.

• x = 2
• x = 3
• x = 8
• x = 64

Solve the equation for x.

• 2.41
• x = 12
• x = 33.333
• x = 5.99

Rewrite log_vn = a in exponential form.

• v^a = n
• n^a = v
• vⁿ = a
• aⁿ = v

Change to Logarithmic Form:
5³ = 125

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