University:
Fresno Pacific University
Course:
MATH 210 | Calculus I
Academic year:

2020
Views:

364

Pages:

4
Author:

crawniadxfo

Honors Algebra 2 Name: ____ Date: ____ Period: ____ Chapter 6 Test Review Condense each expression to a single logarithm. 1) 12 log z + 12 log x - 6 log y = log(z^12 * x^12 / y^6) 2) 12 log_8 x - 3 log_8 y - 3 log_8 z = log_8(x^12 / y^3z^3) 3) 6 log_2 a - log_2 c - 6 log_2 b = log_2(a^6 / cb^6) 4) 6 log_9 z + 24 log_9 x + 6 log_9 y = log_9(z^6 * x^24 * y^6) Expand each logarithm. 5) log_6 (a^2 / b^3) = 2 log_6 a - 3 log_6 b 6) log_7(u^6v^4) = 6 log_7 u + 4 log_7 v 7) log_4(c√(ab)) = log_4 c + 1/3 log_4 a + 1/3 log_4 b 8) log_4((x^6/y)^2) = 2(log_4 x - log_4 y) = 2 log_4 x - 2 log_4 y Find the inverse of each function. 9) y = -5 log_2 x + 9 x = -5 log_2 y + 9 x - 9 = -5 log_2 y (-x + 9)/5 = log_2 y y = 2^(-x+9)/5 10) y = log_2(-2x) - 1 x = log_2(-2y) - 1 x + 1 = log_2(-2y) 2^(x+1) = -2y y = 2^(x+1) / -2 11) y = 6 log_2(2x) x = 6 log_2(2y) x/6 = log_2(2y) 2^(x/6) = 2y y = 2^(x/6) / 2 12) y = ((1/3)^x + 4)^(1/2) x = ((1/3)^y + 4)^(1/2) x^2 = (1/3)^y + 4 x^2 - 4 = (1/3)^y y = log_(1/3)(x^2 - 4) 13) y = ((1/2)^x + 8)^(1/3) x = ((1/2)^y + 8)^(1/3) x^3 = (1/2)^y + 8 x^3 - 8 = (1/2)^y y = log_(1/2)(x^3 - 8) 14) y = (4^x + 10)^(1/2) x = (4^y + 10)^(1/2) x^2 = 4^y + 10 x^2 - 10 = 4^y y = log_4(x^2 - 10) Sketch the graph. Then identify the asymptote, domain and range, and state the end behavior. 15) y = log_(1/6)(x+5) + 4 [Image of the graph of y = log_(1/6)(x+5) + 4] Asymptote: x = -5 Domain: x > -5 Range: ℝ End behavior: x → -5⁺, y → ∞ x → ∞, y → -∞ 16) y = log₄(x-1) - 2 [Image of the graph of y = log₄(x-1) - 2] Asymptote: x = 1 Domain: x > 1 Range: ℝ End behavior: x → 1⁺, y → -∞ x → ∞, y → ∞ Rewrite each equation in logarithmic form. 17) 12² = 144 log₁₂(144) = 2 18) y⁴ = x log_y(x) = 4 Rewrite each equation in exponential form. 19) log₁₂(144) = 2 144 = 12² 20) log₂(1/8) = -3 1/8 = 2⁻³ Solve each equation. 21) log₃(x-8) = 1 3¹ = x - 8 3 = x - 8 x = 11 22) ln(3x) - ln(10) = 5 ln(3x/10) = 5 3x/10 = e⁵ 3x = 10e⁵ x = 10e⁵/3 23) log₆(x+30) + log₆(3) = 1 log₆(3x+90) = 1 3x + 90 = 6¹ 3x = -84 x = -28 24) ln(16) + ln(4x) = 1 ln(64x) = 1 64x = e¹ x = e/64 Solve each equation. Round your answers to the nearest ten-thousandth. 25) 4^(2x+2) = 26 2^(4x+4) = 2⁶ 4x + 4 = 6 4x = 2 x = 0.5 26) 8^(1-x) = 5.25 2^(3-3x) = 5.25 3 - 3x = log₂(5.25) -3x = log₂(5.25) - 3 x = -0.2926 27) -6e^(-6n-6) + 5.9 = 58 -6e^(-6n-6) = 52.1 e^(-6n-6) = -52.1/6 No solution 28) -2e^(2x+9) - 1 = -94 -2e^(2x+9) = -93 e^(2x+9) = 93/2 2x + 9 = ln(93/2) 2x = ln(93/2) - 9 x = -2.5803

Chapter 6 Test Review Answers

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