Properties of Logarithms

Write as one logarithm, then simplify.

log₆3 + log₆2

• 0

• log₆5

• log₆1

• 1

Answer explanation

$\log_6\left(2\right)+\log_6\left(3\right)=\log_6\left(2\cdot3\right)=\log_6\left(6\right)=1$

Evaluate log₄1

• 1
• 0
• 4
• undefined

Write the logarithm expression as a single logarithm

log₅4 + log₅3

• log₅7

• log₅12

• log₇5

• 3log₅4

Answer explanation

$\log_5\left(4\cdot3\right)$

Write the logarithm expression as a single logarithm

log₄60 - log₄4 + log₄x

• log₄15

• log₄15x

• log₄56x

• xlog₄30

Answer explanation

$\log_4\left(60\div4\cdot x\right)$

Expand the logarithm expression

log 6x³y

• log 6x³ + log y

• log 6 + log x³ + log y

• 3 log 6 + log x + log y

• log 6 + 3log x + log y

• log 5x + log 4y

• log 5x - 4log y

• (log 5 + log x) - (log 4 + logy)

• 5log x - 4 logy

Evaluate.
log₃81

• 4
• ¹/₄
• -4
• -¹/₄

Expand the logarithm expression

log₅5x^-5

• -5(log₅5x)

• -5log₅5 + log₅x

• log₅25x

• log₅5 - 5log₅x

Evaluate the following logarithm:

log₃27

• 3

• 2

• -3

• ¹/₃

Evaluate the following logarithm:

log₅5

• 1

• 0

• -1

• ¹/₂