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# REVIEW 7-2

REVIEW 7-2. Exponential Functions.          3        -----                             3x - 4  . Find the derivative:.  1. f(x)  =  ln(3x - 4).   2. f(x)  =  ln[(1 + x)(1 + x2) 2 (1 + x3) 3 ]. ln(1 + x) + ln(1 + x 2 ) 2 + ln(1 + x 3 ) 3. ln(1 + x) + 2 ln(1 + x 2 ) + 3 ln(1 + x 3 ).

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## REVIEW 7-2

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1. REVIEW 7-2 Exponential Functions

2.          3       -----                            3x - 4   Find the derivative:  1. f(x)  =  ln(3x - 4)   2. f(x)  =  ln[(1 + x)(1 + x2)2(1 + x3)3 ] ln(1 + x) + ln(1 + x2)2 + ln(1 + x3)3 ln(1 + x) + 2 ln(1 + x2) + 3 ln(1 + x3)                          1                 4x                   9x2          f '(x)  =   ------     +     --------      +     --------                           1 + x            1 + x2             1 + x3

3. 3. y = ln(cosx + 8x) -sinx + 8cosx + 8x 4. y = ln(ln12x) 1__x__ln12x 1__xln12x = 5. y = 9xln2x 9x(1/x) + 9ln2x 9 + 9ln2x

4. 6. y = ex2 7. y = sin(e3x).

5. SOLVE: 8. ln (x + 4) + ln (x - 2) = ln 7 ln (x + 4)(x - 2) = ln 7 eln (x + 4)(x - 2) = eln 7 (x + 4)(x - 2) = 7 x2 + 2x - 8 = 7 x2 + 2x - 15 = 0 (x - 3)(x + 5) = 0 x = 3 or x = -5

6. 9. Solve the equation. e3x + 2 = 40 ln e 3x + 2 = ln 40 (3x + 2) ln e = ln 40 Remember that ln e = 1. 3x + 2 = ln 40 3x = ln 40 - 2

7. 10. Solve for y: ln y2 +3y - ln (y + 3) = 6 y2 + 3yy + 3 ln = 6 ln(y) = 6 y = e6

8. SIMPLIFY: 11. ln(e3x) 12. e2ln5x 13. eln7x+9 14. ln( ) 3x (5x)2 = 25x2 _1_e2x eln7x + e97xe9 -2x

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