algebra 2 lesson 6

x = -2

Solve e-x = e2x+6

x = 11

By converting to an exponential expression, solve log2 (x + 5) = 4

log9 (11/7)4

Condense to a single logarithm: 4 log9 11 - 4 log9 7.

ln (x y1/3 z1/3)

Condense to a single logarithm: ln x + (1/3) ln y + (1/3) ln z.

44 = 256.

Convert the logarithm to exponential form: log4 (256) = 4.

Exponential decay

Does the function f(x) = (0.68)x represent exponential growth, decay, or neither?

Exponential decay

Does the function f(x) = 25e-2x represent exponential growth, decay, or neither?

9 log7 x - 3 log7 y.

Expand log7 (x3/y)3

1/16, 4, 16

Given f(x) = (1/4) -x, evaluate f(-2), f(1), and f(2).

1/25, 1, 625

Given f(x) = 52x, evaluate f(-1), f(0), and f(2).

log 10,000 = 4

Given that 104 = 10,000, write this in logarithm form.

log3 9 = 2

Given that 32 = 9, write this in logarithm form.

ln 120 = 4.78749 . . .

Given that ex = 120, write this as a logarithm, and find the value of x. (Use a calculator)

g(x) = -(log6 x - 4)

Given that f(x) = log6 x, write a function that translates f(x) down 4 units and then reflects it across the x axis.

g(x) is translated up 5 units compared to f(x)

Given the two functions, which statement is true?f(x) = 3x, g(x) = 3x + 5

g(x) is translated right 2 units compared to f(x)

Given the two functions, which statement is true?f(x) = ex, g(x) = ex-2

g(x) is shrunk vertically by a factor of ½ and shifted to the left 4 units compared to f(x).

Given the two functions, which statement is true?f(x) = log15 x, g(x) = ½ log15 (x + 4)

Yes, since log(2) and log(5) both exist as valid values for the logarithm.

Is x = 0 a valid potential solution to the equation log(x + 2) + log(x + 5) = 1? (You don't need to solve this equation, just determine if x = 0 is a valid solution)

x = 0

Solve for x: log2(x + 2) + log2(x + 1) = 1.

x = 4⁄3

Solve log2(3x) + log2 (4) = 4.

57.55 g

Suppose that you begin with 10 grams of magic crystals, and your crystals grow at a continuous rate of 25% every day (that's why they're magic). How many grams of crystals will you have after one week (7 days)?

8.12 kg

Suppose you have 60 kg of a radioactive material that decays 50% of its mass every year. How much material will you have left after 4 years?

6 ln x + 3 ln y

Using the product and power properties of logarithms, expand ln (x6 y3).

irrational

What kind of number is e?

2.71828 . . .

What's the approximate value of e?

f(x) = (2/3)x

Which of the following is the figure most likely the graph of?