6.4 LogFunctions

# 6.4 LogFunctions - y →-∞ Increasing one-to-one(1 0(a 1...

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6.4: Logarithmic Functions The inverse function of y = f(x) = a x is x = a y , which is equivalent to the logarithmic function y = log a x . This equivalence is used to convert between logarithmic and exponential functions. If the base is the number e , then x = e y if and only if y = ln x . Write the equation in logarithmic form: 1. 16 = 4 2 2. a 3 = 2.1 3. 8 2/3 = 4 4. e 2.2 = M Write in exponential form: 5. log b 4 = 2 6. log 2 6 = x 7. log 3 N = 2.1 8. ln x = 4 Evaluate; if a u = a v , then u = v: 9 . log 8 8 10. log 3 9 1 11. log 5 25 3 12. ln e 3 y = log a x or x = a y Domain Range x-intercept Vertical asymptote Charac- teristic Passes through a > 1 (0, ) (- , ) (1, 0) y-axis as

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Unformatted text preview: y →-∞ Increasing, one-to-one (1, 0) (a, 1) 0 < a < 1 (0, ∞ ) (-∞ , ∞ ) (1, 0) y-axis as y →∞ Decreasing one-to-one (1, 0) (a, 1) Graph the following logarithmic functions; state the domain, range, and any vertical asymptote: 13. y = log 3 x 1 4. y = log 1/2 x 1 5. y = ln x y = log 3 (x – 1) y = 2 + log 1/2 x y = 3 – ln (x + 2) x - 1 = 3 y y – 2 = log 1/2 x ln (x + 2) = 3 - y x = 3 y x = 3 y +1 x = ( 1 / 2 ) y x = ( 1 / 2 ) y-2 x ≈ e y x ≈ e 3-y- 2 2 1 1 1 3 1 1 2 2 2 4 2 2-1-1-1 1-1 3-2-2-2-2 4-3-1...
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6.4 LogFunctions - y →-∞ Increasing one-to-one(1 0(a 1...

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