Rewriting Logs and Exponentials

Evaluate:
log₄16

• 2
• 4
• 1/2
• -2

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

Rewrite 3⁴ = 81 in logarithmic form.

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

Write in exponential form.
log₂32 = 5

• 2^-5 = 32
• 2³² = 5
• 2⁵ = 32
• 32⁵ = 2

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

Solve for x
log₈(x) = 2

• x = 256
• x = 64
• x = 16
• x = 32

Solve for x
5^x = 17

• x = log₁₇5
• x = log 5 + log 17
• x = log₅17
• x = (log 5)/(log 17)

Factor completely: 0.25x + 4.75

• 0.75(x + 4)
• 0.25(x + 19)
• 0.5(0.5x + 9.5)
• 0.25(x + 4.5)

log₄1 = 

• 0
• 1
• 4
• DNE