Recap Law of Logs

Write the logarithm expression as a single logarithm

log₅4 + log₅3

• log₅7

• log₅12

• log₇5

• 3log₅4

Expand the following logarithm: 
log₂ 5x.

• log₂ 5 - log₂ x 
• log₂ 5 + log₂ x 
• 2log 5 + 2log x
• log5 2 + log_x 2

Write log_b(x/y) as two logs

• log_bx-log_by
• log_bx+log_by
• log_bx*log_by
• log_bx/log_by

Rewrite log_b(xⁿ)

• nlog_bx
• (log_bx)ⁿ
• xⁿlog_bx
• log_b(xⁿ)

Simplify: 2log(x) + 3log(xy)

• log(x⁵y³)
• log(5xy)
• 5log(x²y)
• log(6x²y)

If 3^x = y, which of the following is true?

• log₃y = x
• log₃x = y
• log_xy = 3
• log_y3 = x

If log_a8 = b, which of the following is true?

• a^b = 8
• b^a = 8
• a⁸ = b
• 8^b = a

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

Expand.

• 1/3 log x + log y + log z
• 1/3 log x + 1/3 log y + 1/3 log z
• 1/3 log x - 1/3 log y - 1/3 log z
• 3 log x + 3 log y + 3 log z