Logarithms

Evaluating Logs

100

log₅ 125 

x = 3 

200

log₂ 16 

x = 4 

300

log ₃ (1/243) 

x = -5

400

log₆ (1/216) 

x = -3

500

log₃₄₃ 7

x = (1/3) 

Condensing/Expanding

100

Condense: log₃(5) + log₃ (8) - log₃ (2)

log₃(20)

200

Condense log3−log4+log5−log6

log(5/8)

300

Expand: log_b(6x/y)

log_b6 + log_bx − log_by

400

Expand:  ln(x⁴y/7)

4ln(x) + ln(y) − ln(7)

500

Condense: 2(log4 + log 2) 

log 64

Solving logs

100

log 2 + log x = 1

5

200

log −m + 2 = 4

-100

400

log ₉ (x + 6) − log ₉ x = log ₉ 2

6

500

log ₅ 6 + log ₅ 2x ² = log ₅ 48

{2, −2}

Rewrite as log

100

81^(1/2)=9

log₈₁9 =(1/2) 

200

16² = 256 

log₁₆256 = 2 

300

7² = 49 

log₇49 = 7 

400

12² =144

log₁₂144 = 12 

500

x^y = 178 

log_x178 = y

mixed

100

Find the explicit formula: 

a₁ = 28, d = 10

a_n = 28 + (n-1)10 

200

Find  the explicit Formula 

a ₁ = −38, d = −100

a _n = 62 − 100n 

or 

a_n = -38 + (n-1)(-100) 

300

Simplify: 2y ² ⋅ 3x

6y ² x

400

4v ³ ⋅ vu ²

4v⁴ u² 

500

(4xy) ⁻¹

(1/4xy)