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Unformatted text preview:extraneous solutions.
Solve each exponential or logarithmic equation. Give answers to three decimal places. Remember to check for
11. e2x4-3 = 5x
X-3=0 2X+1=O
2 x - 3= 5x
14. 4e2x - 3 = 25
2X=-1
2x 2-5x-3= 0
yet- 28
1X = -1/2
2 x2 +x - Cox - 3:0
e 2x - 7
x ( 2X+ 1) - 3(2x+1 ) = 0
x=-31 64-49-03
2x = In 7
(2*+1)( x-3)=0
x = InZ
12. In(4x) + In(2 + x) = 2
1 x - 83 Vulbez
X 0.973
In (4x ) (2+x)= 2
15. log4 (3x + 1) = 2
4x ( 2+* ) = e2
42= 3x+1
16=3x+1
4 x 2+8 x-2 2 = 0
15- 3X
or
15-X
13. 8 = 53x-2
109 5 8= 3x - 2
16. 272x = 33x+5
272 = 729 = 36
2+ 1095 8 = 3x
2+ 109 - 8 = X
ex = 3x+ 5
3x= 5
1.097 ~X
x = 5/3
the money to triple?
17. If $7,500 is invested in a savings account at a rate of 3.2% compounded semiannually, how long will it take for
22560= 7500(14 2:023) 26
1= 3.2 /100
2
22500= (1+06016)
V = 0.032
7560
3= 1.010#2
2 in ( 1. 016 )
2 34. 6 years or 2 34 years
and 7 months
18. How much energy, in joules, does an earthquake emit which measures 7.3 on the Richter scale?
109 , 0 I = 14. 4 + 1. 5(7. 3)
109 I= 15.35
10 109107 = 10#-35
I = 1015.38
joules = 2.24 * 10" joules
19. A loaf of bread is taken out of hot oven with a temperature of 375'F and placed on a cooling rack with a
surrounding temperature of 72F. After 15 minutes, the temperature of the bread is 215 F. What will the
temperature of the bread be 30 minutes after taking it out of the oven? (Recall Newton's Law of Cooling Warming
is T = Ts + (To - Ts)e-kt.)
-15X
215 = 72+ ( 375 - 72 ) @
T = 72+(375- 72 )e
-0.5(30)
143= (303) p - 15x
143 - e
ISK
T = 72+(303)e
-16
TX 72 F
In ( 203 ) = - ISK
(72-00009269)
K =
In 203
-15
K . 05