PC 12 Expo and Log Review

Skill 5

100

What is the asymptote of y = 2^x

y=0

200

Find the logarithmic equation of the inverse function.

y = 15^x

y = log₁₅ x

300

Write a sentence explaining what this equation says, then evaluate it.

log₃ (1/81) = x

x = -4

400

Determine the value of x.

log_x 128 = 7 

x = 2

500

Evaluate and explain a shortcut you could use and provide an additional example.

log 10⁴²

If the base is not stated then the log has a base of 10. 

Exponential form 10^x = 10⁴²

This means that x has to equal 42.

Shortcut: If the base and the argument are the same number then the answer will be the exponent on the argument, 42!

Another example log₂2⁵ = 5

Skill 6

100

Tell me all characteristics of this function.

y = log_(0.5) x

Asymptote: x = 0

Decreasing Function from Q1 to Q4

Domain: {x|x>0, xER}

Range: {y|yER}

200

Describe the transformations using words. Find its x-intercepts (if any), asymptote(s), domain and range.

y = log₃(x+5) - 1

Intercepts: (-2,0) 

Asymptote: x =-5

Domain = {x|x>-5, xER}

Range = {y|yER}

300

Explain the transformation put on this logarithmic equation in sentences.

y = 2 log₃ 2 (x+9)

The 2 in front of the log means there is a vertical stretch of 2.

The 2 after the log means there is a horizontal stretch of 1/2.

The +9 inside the bracket means the equation moves left 9 on the x axis. 

400

What is the letter "e" called in math and what would its graph's characteristics look like?

y = e^x

"e" is called eulers number and it is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.

Characteristics

Asymptote: y = 0

Domain: {x |xER}

Range: {y | y > 0, y ER}

Increasing from Q2 to Q1

500

Why is y = ln x different than y = log x?

The difference between log and ln is that log is defined for base 10 and ln is denoted for base e. Ln is the inverse of y = e ^x

Skill 7

100

Evaluate.

log_a1 = x

x=0

200

Evaluate.

log₅25 - log₅5

1

300

Evaluate:

10^{log e}

e

400

Expand 

log₅ (xy)^1/2

1/2log₅x + 1/2log₅y

500

Evaluate 

2log₃6 - 1/2log₃64 + log₃2

2

Skill 8

100

Solve for x. State the restrictions.

log₁₀₀(4x)+ log₁₀₀ (3) = log₁₀₀(12)

Restrictions x>0

x=1

200

Solve for x and state restrictions.

2 =log₃(x+3) + log₃(2x-1)

Restrictions: x> -3, x>1/2 so x>1/2

x=3/2

300

Solve for x. State Restrictions.

ln(x-8) + ln (x-10) = ln 60x

Restrictions x>10

x=40

400

Solve for x.

3^x = 5^x-3

x =9.45

500

Solve for x:

log₉x = log₉(x+1) +1/2

x=2/3

Restrictions: x>0

Random Trivia

100

What is Mrs. Bhathella's favorite color?

Purple

200

Who created the letter e in math?

Leonhard Euler

300

What is the singular of "spaghetti"?

Spaghetto

400

What number has the same amount of letters in it as its meaning?

Four

500

What only prime number that contains the letter "e"?

Two