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1. If f(x) = 3x + 6, then find f ^-1(x).
   Solution: y=3x+6; swap y and x: x=3y+6; solve for y: y=(x-6)/3, and f^-1(x)=(x-6)/3
   
   
2. Determine if the following functions are inverses of each other:
   f(x) = 7x + 14
   g(x) = (1/7)x - 2
   Solution: Find composite (fog)(x)= 7((1/7)x - 2) + 14=x-14+14=x - yes these functions are inverse
   
   
3. Write the exponential equation y = 3^x in logarithmic form.
   Solution: log y= log 3^x  = x log 3 or log₃ y= log₃ 3^x  = x log₃ 3=x i.e.  log₃ y=x
   
   
4. Write the logarithmic equation log₇x = y in exponential form.
   Solution: x = 7^y
5. Use the change-of-base formula to convert x=log₄80 to common logarithms.  Then use a calculator to round the value of x to the nearest thousandth.
   Solution: x=log₄80= log80/log4= 1.903/0.602=3.161
    
   
6. Find the amount of money accumulated if you invest $40,000 at 6% interest compounded quarterly for 5 years.  Round your answer to the nearest cent.
   Solution: A=P(1+r/n)^nt i.e. A=$40000*(1+0.06/4)^4*5 = $40,000*1.282=$51,281.49
   
   
7. Find the amount of money accumulated if you invest $40,000 at 6% interest compounded continuously for 5 years.  Round your answer to the nearest cent.
   Solution: A=P*exp(rt)= $40,000*exp(0.06*5)=$40,000*1.35=$53,994.35
   
   
8. Solve the following exponential equation:
   5^x = 2
   Round your solution to the nearest hundredth.
   Solution: apply log to both sides log5^x = log 2 or x*log5=log2 and x= log2/log 5=0.301/0.699=0.431
   
   
9. Solve the following exponential equation:
   e^2x = 18
   Round your solution to the nearest hundredth.
   Solution: apply natural log to both sides 2x=ln 18 or x=1/2*ln18=2.89/2=1.445
   
   
10. Solve the following logarithmic equation:
    log₅x + log₅(4x+5) = 3
    Be sure to check all of your solutions in the original equation.
    Solution: log₅x(4x+5) = log₅ 5³
    or x(4x+5)=125 i.e 4x² +5x-125=0 using quadratic formula: x=5 and x=? - let you practice your quadratic formula skills
    
    

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