Module 8 Algebra II Test Review

Simplify log343 49.

2/3

Identify the logarithmic form of 7^3 = 343.

log7 343 = 3

Express log8 256 − log8 4 as a single logarithm and simplify.

log8 64 = 2

Solve log2 (10x + 5) − log2 5 = 5.

x = 15.5

Solve 3^4x − 1 = 9^x + 1.

x = 3/2

2x^2 + 5x - 3 / x + 3 = 7

x = 4

Solve 2^2x − 2 = 15. Round your answer to the nearest hundredth.

x ≈ 2.95

Use a table and graph to solve the equation.log (x + 2) − log 3 ≥ log 12

x ≥ 34

Solve log35 (x + 3) + log35 (x + 5) = 1.

x=2

Write the inverse variation function given that y varies inversely with x, and y = 2 when x = 8.

y = 16/x

Write the direct variation function given that y varies directly with x, and y = 16 when x = 4.

y = 4x

Simplify ln e ^−12t .

−12t

Simplify. Identify any x-values for which the expression is undefined. 2x^2 + x - 3 / x - x^2

- 2x+3 / x ; x does not = 0 , 1

Calculate log625 ^ 5 using mental math.

0.25

The pressure P of a gas varies directly with the temperature T and inversely with the volume V. A certain gas has a volume of 6 liters (L), a temperature of 400 Kelvins (K), and a pressure of 2.4 atmospheres (atm). If the gas is expanded to a volume of 15 L and is heated to 650 K, what will the new pressure be?

1.56 atm

The time taken for a journey on a motorway varies inversely as the average speed for the journey. The journey takes 1.5 h when the average speed is 54 miles per hour. Identify the time taken in hours for this journey when the average speed is 45 miles per hour.

1.8 h

What change do you have to make to the graph of f (x) = 11x in order to graph the function g (x) = 11x + 12?Shift the graph _____ units _____.

12, up

The loudness L of sound in decibels is given by L = 10 log (l/l0) where l is the intensity of sound, and l0 is the intensity of the least audible sound. If l0 = 10^-12 W/m^2. about how many times more intense is a 97 decibel sound than a 93 decibel sound?

2.5

Identify the exponential form of log2 0.25 = −2.

2^−2 = 0.25

The power P required to do a fixed amount of work varies inversely as the time t. If a power of 15 J/h is required to do a fixed amount of work in 2 hours, what is the power required to do the same work in 1 hour?

30 J/h

Divide. Assume that all expressions are defined. 10b^2 - b - 3/ 5b^2 + 28b + 15 divided by 1 - 4b^2 / 20b^2 + 12b

4b(5b - 3)/ (1-2b) (b + 5)

The value of y varies directly with x, and y = 343 when x = 49. Find y when x = 8.

56

Calculate log 1000000 using mental math.

6

The profit of a company, currently $35,000 grows at the rate of 5% per year. The amount P after t years can be expressed by the exponential equationP = 35000(1 + 0.05)t. Identify the number of years it will take for the profit toexceed $46,500.

6

Simplify log5 625^2.

8

The volume V of a cone varies jointly as the area of the base B and the height h. V = 32 cm3, when B = 16 cm2 and h = 6 cm. Identify h when V = 60 cm3 and B = 20 cm2.

9 cm

A relation consists of the following points. Identify the domain and range of the inverse relation. x 0 1 3 5 7 y 2 3 5 8 10

D: {2, 3, 5, 8, 10} R: {0, 1, 3, 5, 7}

Identify the domain and range of the inverse of f(x) = 0.5x.

D: {x ∣ x > 0} R: ℝ

Given the function g(x) = 43x + 3, identify the correct description of the graph's transformation from the graph of its parent function.

The graph of g(x) is a horizontal compression of f(x) = 4x by a factor of 1/3 and a shift 3 units up.

Using an exponential model for the data, estimate when the population will exceed 100 million. year 2000 2002 2004 2006 population 53 57 62 67

The population will exceed 100 million in 2017.

Peter bought an antique piece of furniture in 2000 for $10,000. Experts estimate that its value will increase by 12.12% each year. Identify the function that represents its value. Does the function represent growth or decay?

V(t) = 10000(1.1212)t; growth

The value of a camcorder bought new for $2000 decreases 20% each year. Identify the function for the value of the camcorder. Does the function represent growth or decay?

V(t) = 2000(0.8)t; decay

Determine whether f is an exponential function of x. If so, find the constant ratio. x -1 0 1 2 f(x) 1/4 1/2 1 2

f is an exponential function with a constant ratio of 2.

Identify the graph of the function f(x) = 2x − 5. Then identify its inverse and the graph of the inverse.

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

Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 2, reflected across the x-axis, and shifted by 4 units right.

g(x) = −2ln (x − 4)

The radius of a cone is 28 cm. The volume is given by the formula V=1/3(28^2)h where h is the height of the cone. Identify the inverse of this function and use it to fine the height of the cone, if its volume is 5488 cm^3

h= 3V/784; 21 cm