Log Properties

Product Property

100

Expand: log8x

log8+logx

200

Condense: ln6+lnx+lny

ln6xy

300

Expand: log (xyz)

log (x) + log (y) + log (z)

400

Expand (using multiple rules): log₄ (x²y³)

2log₄x + 3log₄y

500

Challenge (expand): log2x^-3

log2-3logx

Quotient Property

100

Expand: ln(4/x)

ln4-lnx

200

Condense: log₆ a - log₆ b

log₆(a/b)

300

Expand: ln (3/xy) 

ln3-lnx-lny

400

Condense (using multiple rules): 1/2log₂ab - log₂c - log₂d

log₂ (√ab / cd)

500

Condense (using multiple rules): ln(x+4) - 3lnx - lny

ln (x+4 / x³y)

Power Property

100

Expand: logx³

3logx

200

Condense: 7logx

logx⁷

300

Condense (using multiple rules): 4log₂a + 9log₂b

log₂(a⁴b⁹)

400

Expand (using multiple rules): log₃ (a²√b / cd⁵)

2log₃a + 1/2log₃b - log₃c - 5log₃d

500

Expand: 1/3 (log₈a + 2log₈b)

log₈∛ab²

Using Multiple Rules

100

Expand: log8x⁴y

log8+4logx+logy

200

Condense: 2logk + 4logh - 5logj

log (k²h⁴/j⁵)

300

Condense: 2log₄a+2log₄b

log₄(a*b)²

400

Condense: log₆t - 4log₆h

log₆(t/h⁴)

500

Expand: ln (r⁴t⁶/v)

4lnr + 6lnt - lnv

Random

100

Condense (without solving, answer should be in log form): log₂96-log₂3

log₂32

200

When there is no visible subscript, what is the base?

10

300

What does ln mean?

natural log

400

What number does e represent?

2.718281828

500

What does natural log (ln) mean?

log_e