Logarithms

Rewriting Expressions

100

Write in logarithmic form

14⁰=1

log₁₄1=0

200

Write in exponential form

log₁₉361=2

19²=361

300

Write in exponential form

log₅(1/125)=-3

5^-3=(1/125)

400

Write in logarithmic form

14^-2=(1/196)

log₁₄(1/196)=-2

500

Write in logarithmic form

256^1/2=16

log₂₁₅16=1/2

Evaluating Logarithms (no calc)

100

log₃9

2

200

log₅125

3

300

log 100

2

400

log₁₄₄(1/12)

-1/2

500

ln (e³)

3

Evaluating Logarithms

100

Round to the nearest thousandth

log₄29 

2.429

200

Round to the nearest thousandth

log₃6.9

1.758

300

Round to the nearest thousandth 

log 423

2.626

400

Round to the nearest thousandth

Ln 30

3.401

500

ln(-5)

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Solving Logarithmic Equations (no calc)

100

Solve for k

log k = -1

k= 1/10

200

Solve for r

log₄(r-4) = -1

r = 17/4

300

Solve for v

log₅v + 10 = 10

v=1

400

Solve for n

-6 + log₁₁(n+5) = -5

n = 6

500

Solve for x

log₂(-40+3x²) = log₂(4x²+14x)

x = -4, -10

Solving Exponential Equations

100

Solve for x

8^x=64

x=2

200

Solve for n (round to the nearest ten-thousandth)

13ⁿ=62

n=1.6091

300

Solve for v (round to the nearest ten-thousandth)

13^v+4 =23

v=-2.7776

400

Solve for p (round to the nearest ten-thousandth)

18^p +1 = 65

p=1.4389

500

Solve for v (round to the nearest ten-thousandth)

-8(15^v)=-43

v=.6210