Logarithm

Simplify

100

log₂8

3

200

log₃81

4

300

log₅125 + log₅25

5

400

log₂64 - log₂8

3

500

log₄64 + log₄16 - log₄4

4

Solving

100

log₂(x)=5

x=32

200

ln(x)=1

x=e

300

Log₃(x)+Log₃(x-2)=1

x=3, x=-1 is extraneous

400

Log(x²)=Log(4x-4)

x=2

500

(Log₂(x))²-Log₂(x³)-4=0

x=16 or x=1/2

Graph

100

What is the x-intercept of the basic parent function f(x) = log₃(x)?

(1,0)

200

If the graph of f(x) = log₂(x) is shifted 5 units to the left and 2 units up, what is the equation of the new graph?

g(x) =log₂(x + 5) + 2

300

What is the equation of the vertical asymptote for the graph of f(x) = log(x - 4) + 7?

x=4

400

If the graph of f(x) = ln(x) is reflected across the y-axis, what is the domain of the new function?

x<0 

500

A logarithmic function of the form f(x) = log_b(x - h) has a vertical asymptote at x = -3 and passes through the point (1, 2). What is the base $b$ of this logarithm?

b=2

Expand

100

log(xy)

logx + logy

200

log(x/y)

logx - logy

300

log(x⁴)

4logx

400

log(x³y²/z)

3logx + 2logy - logz

500

log((ab²)³/c⁴d)

3loga + 6logb - 4logc - logd

Condense

100

Log x + Log y

Log(xy)

200

2Logx

Log(x²)

300

Log x - Log y

Log(x/y)

400

3Logx + 2Logy

Log(x³y²)

500

2Log a + 3Log b - Log c - 4Log d

Log(a²b³/cd⁴)