Test 9 Review

Expand the following:  $\log\left(j^4k^7\right)$  

•  $\log\left(4j\right)+\log\left(7k\right)$  

•  $11\log\left(j+k\right)$  

•  $28\log\left(jk\right)$  

•  $4\log\left(j\right)+7\log\left(k\right)$  

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

Write in exponential form.
log₂32 = 5

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

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Rewrite 3⁴ = 81 in logarithmic form.

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

Solve for x:
log_x 25 = 2

• 5
• -5
• 1/5
• -1/5

Solve for x.
3^x = 27

• 2
• 4
• 3
• 5

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

Sovle for x:
5^{-3x - 1} = 25

• x = -1
• x = -4
• x = -3
• x = 1

Solve 3³ = 3^{4x + 2}

• x = ¼
• x = -¼
• x = ½
• x = -½