Senior Trig Unit 2 Test

log6 x + log6 (2x + 1) = log6¹⁵

(5/2)

2m⁻⁸n³ / 6(m⁴n⁶)³

1 / 3m²⁰n¹⁵

Solve 1) 3ˣ < 40 2) log4 x < 2 3) log(x+3) < 2 4) eˣ < 3 5) 3log2 x - 12 > 6

1) {x | x < 3.358} 2) {x | 0 < x < 16} 3) {x | -3 < x < 97} 4) {x | x < 1.099} 5) {x | x > 64}

9ˣ⁻¹ / 3³ˣ⁻²

1/3ˣ

7ˣ⁻¹ = 2³ˣ

125

Graph each function. Make a table with 5 critical points (create asymptotes for each) 1a. f(x) = 2ˣ 1b. g(x) = 2ˣ⁺⁵ - 3 2. f(x) = eˣ 3. g(x) = log3ˣ

1a. Asymptote: y = 0, D: negative/positive infinity, R: y>0 (-2, 1/4), (-1, 1/2), (0, 1), (1, 2), (2, 4) 1b. Asymptote: y = 0, D: negative/positive infinity, R: y>0 left 5 down 3 2. Asymptote: y = 0, D: negative/positive infinity, R: y>0 (-2, 1/7.4), (-1, 1/2.7), (0, 1), (1, 2.7), (2, 7.4) 3. Asymptote: y = 0, D: x>0, R: negative/positive infinity

Evaluating Logarithmic Expressions: 1) log5²⁵ 2) log25⁵ 3) log1/5²⁵ 4) log7¹ 5) log6⁶ 6) log1000 7) ln e

2 1/2 -2 0 1 3 1

8√⁶ * 4√⁵⁴

2 ⁹√⁶

(15x³y⁴)⁻²(5x⁸y⁻⁴)²

25x¹⁰ / 15²y¹⁶

Rewrite each logarithmic equation in exponential form: 1) log2 x=4 2) log1/4 x=-1

2⁴ = x 1/4⁻¹ = x

Simplify 4x ⁻²/⁵

4 5√x³ / x

Find the percent increase or decrease 1) ORIG: $50 NEW: $70 2) ORIG $90 NEW: $72

40% increase 20% decrease

(6√²)√⁵

6 √⁷

Simplify (4xy)²(x²y)³ / 10x³y⁷

8x⁵ / 5y²

Tell whether each function represents exponential growth/decay: 1) y = 4ˣ 2) y = (1/2)ˣ 3) y = 2eˣ 4) y = e⁻ˣ

Growth Decay Growth Decay

Find the composition of the given functions f(x) = x² + 2x - 5 g(x) = 2x - 3 Find: A) [f o g] (4) B) [f o g] (x)

[f o g] (4) = 30 [f o g] (x) = 4x² - 8x - 2

Prove if the functions are inverse using a composition of functions f(x) = 2x - 9 g(x) = x/2 + 9

f(x/2 - 9) = x + 9 g(2x-9) = x + 4.5 f(x) and g(x) are not inverses

Write the inverse 1) f(x) = 6ˣ 2) f(x) = e³ˣ + 4 3) h(x) = log(x-3) 4) g(x) = 3ˣ + 2

f-1 = log6ˣ f-1 = f-1 = 10ˣ + 3 f-1 =

Rewrite using base change formula 1) log3⁷ (common log) 2) log7³ (natural log)

log 7 / log3 ln 3 / ln 7

Rewrite each exponential equation in logarithmic form 1) 5ˣ = 25 2) 6ˣ = 1/216

log5²⁵ log6⁽¹/²¹⁶⁾

Simplify each logarithm using properties 1) log7 x - log7 y 2) log9 n + log9 (n+2) 3) 2log5 x - log5 y 4) 3log7 (2x)

log7 (x-y) log9 (n² + 2n) log5 (x²/y) log7⁸ˣ^³

Solve for x (no calculator) 1) e³ˣ = 5 2) 2ˣ ⁺ ³ = 7

x = 1/3 ln5 x = log2⁷ - 3

log2 (x-3) = 4

x = 19

10 / 2 + 5e³ˣ = 7/8

x = 2.114

4log3x = 32

x = 33333333.333

20ln (7x) = 300

x = 467002.482

2e.³⁵ˣ - 7 = 10

x = 6.114

ln x + ln(x-3) = 4 (quad formula)

x = 9.040

x⁸/³ + 5x²/³ divided by x²/³

x² + 5

(x√² - y√²)²

x²√² - 2xy√² + y²√²

Solve. State the PRRs. Write solution set 2x³ + 3x² + 6x - 4 = 0

{1/2, -1 - i√3, -1 + √3}

2log2 x - log2 (3x-8) = 2

{4, 8}