Evaluate a log5 75 log5 3 b log3 log2 16 c Express logb 5

Evaluate: a) log_5 75 - log_5 3. b) log_3 + log_2 16 c) Express log_b ^5 Squareroot/y^3 z^2 as a sum and/or difference of logarithms. Solve for x: a) log_3 (x + 12) - log_3 (x + 4) = 2, b) 2^x + 1 = 3. Perform the following transformations of f(x) = x^2; a) Shift f(x) up 3 units, b) Shift the result of a) to 2 units right, c) Reflect the result of b) about the x-axis. Find the exact value of the following: a) cos (3 pi/4), (b) tan (5 pi/6). Evaluate the six trigonometric functions at theta = pi/3. Let the trigonometric function f be defined as f(x) = 2 sin(x) (a) What is the amplitude? (b) What is the period? (c) Sketch one period off. Find the values of a and b; Sketch the graph of the function: y = tan(x) and state the domain range of the function. Find the values of the six trigonometric functions of theta such that Cos theta = -4/5, theta lies in Quadrant III

Solution

1) a) (log75/log5) – (log3/log5) = 2.68 – 0.683 = 1.997

b) (log27/log3) + (log16/log2) = 3 + 4 = 7

2)b) 2^(x + 1) = 3

        (x + 1)log2 = log3

       X + 1 = log3/log2 = 1.585

      X = 0.585

4) a) cos(3pi/4) = cos(135) = -0.707

     b) tan(5pi/6) = tan(150) = -0.577

5) sin(pi/3) = 0.866

     Cos(pi/3) = 0.5

     Tan (pi/3) = 1.732

     Cot (pi/3) = 0.577

     Sec(pi/3) = 2

     Csc(pi/3) = 1.155

6) Amplitude = 2

   Period = 2pi

7) a/15 = cos39 =========> a = 11.66

     b/15 = sin39 =========> b = 9.44