Exponential and Logarithm Functions

Simplify/Expand

100

Expand: log(2x)

log(2) + log(x)

200

Simplify: 3log(5)

log(5³)

300

Expand: log₃(a³/b²)

3log₃(a) - 2log₃(b)

400

Simplify: log(x) + log(y) - 2log(z)

log(xy/z²)

500

Simplify: 5log₅(2) + (1/2)log₅(9) - 2log₅4

log₅(6)

True/False

100

True or False: ln(x) = log_e(x)

True

200

True or False: log₄(50) = log(50)/log(4)

True

300

True or False: 2³ has 2 as the index and 3 as the exponent

False: 2 is the base, 3 can be index or exponent

400

True or False: A logarithmic/exponential function, f(x), and its inverse, f^-1(x), become f(f^-1(x)), the function forms a straight line where given log_a(x), y = ax

False: f(f^-1(x)) will linear graph where y = x

500

True or False: An exponential function, either decaying or growing, will eventually intersect a line where x = ∞

False: x will approach infinity but not intersect it

Inverse

100

Find the Inverse: a^x = y

Log_a(x) = y

200

Find the Inverse: f(x) = log₂(x)

f^-1(x) = 2^x

300

Find the Inverse: f(x) = log₅(2x)

f^-1(x) = 5^x/2

400

Find the Inverse: f(x) = 3log(x/2)

f^-1(x) = 2(10^x/3)

500

Find the Inverse: f(x) = 5e^2x

f^-1(x) = (1/2)ln(x/5)

Exponential

100

2^x = 16

x = 4

200

5^x+1 = 125

x = 2

300

e^2x = 7

x = 0.972

400

5e^x - 3 = 17

x = 1.386

500

e^2x + 3e^x - 10 = 0

x = 0.693

Logarithm

100

Log(x) = 2

x = 100

200

ln(x) = 3

x = e³

300

log₅(x - 2) = 2

x = 27

400

2 - 6ln(3x) = 10

x = 0.087

500

ln(x) + ln(x-2) = 1

x = 7