Properties of Logarithms & Equations

Condense

• logxyz³
• log(xy/z³)
• logx+logy+logz³
• logx³y³z³

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

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Change to Logarithmic Form:
12² = 144

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

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log₅(4x-7)=log₅(x+5)

• 3
• 12
• 4
• 7

3^{2x – 6}  = 3⁴

• x = log 4
• x = 5
• x = 4
• x = -1

log₂(2) + log₂(8x) = 6

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• x = 3
• x = 2
• x = 6
• x = 4

log₆(2x + 3) = 3

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• x = 106.5
• x = 100
• x = 16
• x = 50

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