Properties of Logarithms

Rewrite

100

Write this expression in exponential form  log₃81=4

What is 3⁴=81

200

Write this expression in logarithmic form  6^y=18

What is log₆18=y

300

Write this expression in exponential form  log_x7=2

What is x²=7

400

Write this expression in logarithmic form  9^x=36

What is log₉36=x

500

Write this expression in exponential form  log_12xy144=56

What is (12xy)⁵⁶=144

Evaluate

100

Evaluate Logarithm log₇343

What is 3

200

Evaluate Logarithm log₅625

What is 4

300

Evaluate Logarithm log₂1024

What is 10

400

Evaluate log₃(1/243)

What is -5

500

Evaluate log₅(1/625)

What is -4

Expand

100

Expand log₂(9/4)

log₂9 - log₂4

200

Expand log₃(5x)

log₃5 + log₃x

300

Expand log₇(y⁴)

4log₇(y)

400

Expand log(3x⁶/5)

log3 + 6logx - log5

500

Expand log₉(6x²/11y)

log₉6 + 2log₉x - log₉11 - log₉y

Condense

100

Condense log₂6 + log₂8

log₂(6*8) = log₂48

200

Condense log₃10 - log₃5

log₃(10/5) = log₃2

300

Condense 6log₃x

log₃x⁶

400

Condense log₄y + 4log₄x - 9log₄z

log₄(yx⁴/z⁹)

500

DOUBLE JEOPARDY

Condense 2log₉x - log₉y - 3log₉z

log₉(x²/yz³)

Solving Equations

100

Solve: 2^-n = 16

What is n = -4

200

Solve 64^x = 16

What is x = 2/3

300

Solve: 6^(-2x) = 1

What is x = 0

400

Solve: (1/16)^(2x) = 1/64

What is x = 3/4

500

Solve 5(2^-(8r)) = 14.6

What is r = -0.1932