University:
Whitman College
Course:
MATH-126 | Calculus II
Academic year:

2024
Views:

311

Pages:

1
Author:

alkilowyx84

Exponential and Logarithmic Functions Worksheet 1. Solve each equation: (a) 92y−1 = 27y 1/4 (b) 12 = 4b (c) ln(x + 1) − ln(x) = 1 (d) 32t = 161−t (e) log10 (ex ) = 1 x (f) ee = 2 2. Write each expression as a single logarithm. Assume all variables represent positive real numbers. (a) − 34 logx a6 b8 + (b) logb (2y + 5) − 2 9 3 3 logx a b 1 2 logb (y + 3) (c) (logb k − logb m) − logb a (d) 2 loga (z − 1) + loga (3z + 2) (e) loga (pq 2 ) + 2 loga (p/q) 3. Write each of the following expressions as a sum, difference, or product of logarithms (and simplify if possible). Assume that all variables represent positive real numbers. (a) log5 √ 5 7 3 (b) logz x5 y 3 3 (c) logp q 3 m5 n4 t2 (d) log6 (7m − 3q) (e) log3 4p q 4. Differentiate or Integrate, as indicated: (a) (b) (c) (d) (e) d dx d dx d dx d dx d dx 2 3x +sin(x) = 2 log5 (x + e3x ) = logx (3x + 1) = sin−1 (ex ) = 1 ln x1 + ln(x) = x2 + x + 1 dx = x Z x+1 (g) dx = x2 + 2x Z (h) 5t dt = Z 1 (i) dw = w ln(w) (f) Z 1

Exponential and Logarithmic Functions Worksheet

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