Logarithms

Evaluating Logs

100

What is the value of the log?

log₉729

3

200

What is the value of the log?

log₂₆1

0

300

What is the value of the log?

log₂2

1

400

What is the value of the log?

log₃(1/9)

-2

500

What is the value of the log?

ln(1/e⁴)

-4

Condensing Logs

100

Condense:

log(x) - 4log(y)

log(x/y⁴)

200

Condense:

7log(b) + xlog(c)

log(b⁷c^x)

300

Condense:

log_b2 + 3log_b3

log_b(54)

400

Condense:

log_b2 + log_b9

log_b(18)

500

Condense:

log_b(6) - log_b(6)

log_b(1)

Expanding Logs

100

log ( x / y⁵ )

logx - 5logy

200

log ( y²z⁵ / x⁴ )

2logy + 5logx - 4logz

300

log ( x² / zy² )

2logx - logz - 2logy

400

Solve for the numerical value.

loga = 11 logb = -5 logc = 6

log ( c⁷ / a⁸b⁴ )

-26

500

Solve for the numerical value.

loga = -2 logb = -5 logc = 4

log ( b⁶c³ / a³ ) 

-12

1st Degree Logs

100

log₃x = 5

x = 243

200

log₁₂₅x = 4/3

x = 625

300

log₅(9x) + 2log₅(3) = 2

x = 25/81

400

log₂(5x) + 3log₂(2) = 0

x = 1/40

500

log₆(4x) + 2log₆(3) = 0

x = 1/36

2nd Degree Logs

100

log₃(x²-1) - log₃(2x+2)=2

x=19

200

log₃(4x²-1) - log₃(4x+2)=0

x = 3/2

300

log₆(x²+4x+4)=2

x=4 or x=-8

400

log_x+4(3x²-6x)=2

x=8 or x=-1

500

log_x+5(2x²-7x+7)=2

x=18 or x=-1