Logarithm 2.2

A

100

Convert from exponential form into logarithmic form.

10^x=3

log₁₀3 = x

200

log₁₀100 = ???

100 = 10², so

log₁₀100 = 2

200

log₁₀1 = ???

since    10⁰ = 1   , so

log₁₀1 = 0

300

log₂0.25 = ???

Since    0.25 = ¹/₄ = 2^-2  , so

log₂0.25 =-2

400

log₈2 = ???

log₈2 = ¹/₃

B

100

Convert the logarithmic form into exponential form.

log₁₀x = 1.2

10^1.2 = x

200

log₄64 = ???

Since   64 = 4³   , so

log₄64 = 3

200

log₂2 = ???

Since   2¹ = 2   , so

log₂2 = 1

300

log₁₀0.001 = ???

Since   0.001 = ¹/₁₀₀₀ = 10^-3   , so

log₁₀0.001 =-3

400

log₁₀₂₄2 = ???

log₁₀₂₄2 = 0.1

C

100

Convert the logarithmic form into exponential form.

log_y3 = 2

y² = 3

200

log₃243 = ???

Since   243 = 3⁵  , so

log₃243 = 5

200

log₃1 = ???

Since   3⁰ = 1   , so

log₃1 = 0

300

log₄0.25 = ???

Since   0.25 = ¹/₄ = 4^-1   , so

log₄0.25 = -1

400

log₉3 = ???

log₉3 = 0.5

D

100

Convert the logarithmic form into exponential form.

log₂3 = k

2^k = 3

200

log₂128 = ???

Since   128 = 2⁷  , so

log₂128 = 7

200

log₇7 = ???

Since   7¹ = 7   , so

log₇7 = 1

300

log₅0.2 = ???

Since   0.2 = ¹/₅ = 5^-1   , so

log₅0.2 = -1

400

log₁₀₀₀10 = ???

log₁₀₀₀10 = ¹/₃