Logarithms (Properties, Evaluating, Graphing)

Evaluate (No Calculators)

100

log₂(8)

3

200

log₃(1)

0

300

log₇(1/49)

-2

400

log_x64 = 2

8

500

log₆₄(x) = 2/3

1/9

Expand Logs

100

log₃(13y)

log₃(13) + log₃(y)

200

log₆(x²/y)

2log₆(x) - log₆(y)

300

log(5a²b⁶)

log(5) + 2log(a) + 6log(b)

400

log₂(3x²y³ / 10g³)

log₂(3) + 2log₂(x) + 3log₂(y) - log₂(10) - 3log₂(g)

500

log₄(5x²y4⁷ / 6z³)

log₄(5) + 2log₄(x) + log₄(y) + 7log₄(4) - log₄(6) - 3log₄(z)

Condense Logs

100

log₃(a) + log₃(19)

log₃(19a)

200

log₂(a) - log₂(b)

log₂(a/b)

300

4log₃(x) - 3log₃(y)

log₃(x⁴ / y³)

400

log₅(x²) - 2log₅(y) - log₅(z)

log₅(x² / y²z)

500

log₅(3) + 3log₅(a) + 7log₅(b) - log₅(c)

log₅(3a³b⁷ / c)

Solve for x

100

5^2x-1 = 5⁷

x = 4

200

log₄(999) = x

4.982

300

4^7x = 64^x-2

x = - 3/2  or -1.5

400

5(3^x)= 50

Include 3 decimal places

2.095

500

3 * (6^x)-10 = 80

1.898

Logarithm Graph

100

Parent graph: log₂(x)

Write an equation with transformation: 2 units down

log₂(x) - 2

200

Parent graph: log₂(x)

Write an equation with transformation: 3 units to the right

log₂(x-3)

300

Parent graph: log₂(x)

Write an equation with transformation: 5 units left, 3 units down

log₂(x+5) - 3

400

Where is the asymptote for the function:

log₂(x - 2) - 3

x = 2

500

What is the domain and range of the function:

log₂(x + 3) - 250