PRECAL REVIEW DAY 11/14/17
COPY THE FOLLOWING INTO JOURNAL 1 of 3 Transformations of logs Vertical Transformation Horizontal Transformation g x = log b x + c g x = log b x c g x = log b (x + c) g x = log b (x c) Shift graph up Shift graph down Shift graph left Shift graph right Reflection g x = log b x g x = log b ( x) Reflect about x-axis Reflects about y-axis Vertical Stretching or Shrinking g x = c log b x Vertically stretches if c > 1 Vertically shrinks if 0 < c < 1 Horizontal Stretching or Shrinking g x = log b cx Horizontally shrinks if c > 1 Horizontally stretches if 0 < c < 1
COPY THE FOLLOWING INTO JOURNAL 2 of 3 Transformations of exponents Vertical Translation g x = c x + k Shift graph up if k > 0 Shift graph down if k < 0 Horizontal Translation g x = c x+k Shift graph left if k > 0 Shift graph right if k < 0 Reflection g x = c x g x = c x Reflect about x-axis Reflects about y-axis Vertical Stretching or Shrinking g x = kc x Vertically stretches about x-axis by a factor of k Horizontal Stretching or Shrinking g x = c kx Horizontally stretch about y-axis by a factor 1 k
COPY THE FOLLOWING INTO JOURNAL 3 of 3 Important Concepts/Formulas IF log b x = y THEN b y = x ln = natural log e = natural base Compound Interest Formula A = P(1 + r n )nt Continuous Compound Interest Formula A = Pe rt Exponential Growth/Decay N = N 0 (1 + r) t Continuous Exponential Growth/Decay N = N 0 e kt
Evaluate the expression log 3 1 81
ANSWER 4
Solve this equation 25 3x+2 = 125
ANSWER 1 6
Evaluate this equation log 4 16
ANSWER 2
Condense the expression 2 log 4 m + 6 log 4 n 3(log 4 3 + log 4 j)
ANSWER log 4 m 2 n 6 (3j) 3
ANSWER log 4 m 2 n 6 27j 3
Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded daily?
ANSWER $380.48
Expand this expression log 5 x 2 a 7 b *Hint exponent fractions are written in what form?
ANSWER 2log 5 x + 7 log 5 a + 1 2 log 5 b
Evaluate this equation e ln 12
ANSWER 12
Solve this equation 3 x+3 = 27 x 2
ANSWER 9 2
Condense the expression 3 log 3 x 2 log 3 y
ANSWER log 3 x 3 y 2
Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded annually?
ANSWER $375.18
Solve this equation log 6 x + log 6 (x 5) = 2
ANSWER 9
Expand this expression log 3 9x 3 y 3 z 6
ANSWER 2 + 3 log 3 x + 3 log 3 y + 6 log 3 z
Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded continuously?
ANSWER $380.49
Evaluate the expression log 10 12
ANSWER 12
Condense the expression 5 ln(x + 3) + 3 ln 2x 4 ln(x 1)
ANSWER ln 8x3 (x + 3) 5 (x 1) 4
Solve this equation e 2x 8e x + 15 = 0 *Hint what do you do to quadratic equations
ANSWER ln 3 or ln 5
Evaluate this equation log 25 5
ANSWER 1 2
Solve this equation 3 x+8 = 9 2x
ANSWER 8 3
Transformation If f x = 5 x. Then if g x = 5 x 2. What is the transformation?
ANSWER The graph is translated 2 units to the right
Evaluate this equation ln e 11
ANSWER 11
Evaluate the expression 9 log 9 5.3
ANSWER 5.3
Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded quarterly?
ANSWER $379.11
Transformation If f x = 4 x. Then if g x = 4 x. What is the transformation?
ANSWER The graph is translated over the y-axis
Evaluate this equation 3 log 3 9
ANSWER 9
Solve this equation log 2 x + log 2 3 = log 2 18
ANSWER 6
Expand this expression log 6 36xy 2
ANSWER 2 + log 6 x + 2 log 6 y
Expand this expression ln e x 2 y 3 z
ANSWER 1 2 ln x 3 ln x ln z
Evaluate this equation log 2 32
ANSWER 5
Solve this equation e x 4e x = 0
ANSWER ln 2
Transformation If f x = 5 x. Then if g x = 5 x. What is the transformation?
ANSWER The graph is translated over the x-axis
Word Problem You invest $1500 in an account with an interest rate of 8% for 12 years, making no other deposits or withdrawals. What will be your account balance if the interest is compounded monthly?
ANSWER $3905.08
Solve this equation log 2 (x 1) + 1 = log 2 x + 3
ANSWER 5
Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded monthly?
ANSWER $380.03
Evaluate this equation log 13 1
ANSWER 0
Condense the expression 1 3 log 2 a log 2 (b + 1)
ANSWER log 2 3 a(b + 1)