precalc4-exp-logs

precalc4-exp-logs - to graph more general functions...

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Algebra of Exponentials and Logarithms. You should be comfortable with the various rules for simplifying exponentials and logs. 1. Simplify the following. (a) ( x 2 y ) 7+ n ( xy 2 ) n 2 (b) ( x + y ) a + b ( x 2 - y 2 ) a - b (c) ( a 2 b ) 3 b 5 + ( a 3 b ) 4 a 6 (d) log 2 ± 2 a · 8 b/ 5 4 c ² (e) 3 2 10 2 log 5 (f) 5 e - 3 ln 2 (g) 2 3+log 2 2 (h) e (ln 3) / 2 2. Find all values of x satisfying each equation. (a) 10 5+ x = 10 5 + 10 x (b) 10 5+ x = 10 5 · 10 x (c) 10 5 · x = 10 5 · 10 x 3. Find all values of x satisfying each equation. (a) ln(3+ x ) = ln 3+ln x (b) ln(3 x ) = ln 3 + ln x (c) ln(3 x ) = (ln 3)(ln x ) 4. Write the following expressions in terms of log u (or ln u or log b u ) and log w (or ln w or log b w ). (a) log( u 2 w ) (b) log b ( u 3 /w 2 ) (c) ln(1 / w ) (d) log 2 (2 / uw ) Graphing. You should should be familiar with the graphs of y = e x and y = ln x . Even more, you should be able
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Unformatted text preview: to graph more general functions involving exponentials and logs. 5. Sketch a graph of the following functions. Label at least three points on each graph. (a) f ( x ) = 4-log 3 x (b) g ( x ) = 2 x + 1 (c) h ( x ) = 3 e-x + 2 Equations. You should be able to not only simplify expressions, but also solve equations involving exponentials and logs. 6. Solve each of the following equations for x . (Note: At least one of these equations has no solution.) (a) e 3 x = (5 /e ) x +1 (b) 3 x 5 3 x +1 = 0 (c) log x-log( x + 1) = 2 (d) ln x + ln x 2 = 1-2 ln x (e) e x ( e x-5) = 6 (f) 2 e 2 x + 6 = 7 e x...
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This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.

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