MAT220

119. Explain how to solve an exponential equation when both sides can be written as a power of the same base. When an exponential equation has both sides of the equation as the same base one needs to rewrite the equation in the form of bM=bN. For instance, 24x-3=8. To make this the same base we need to make 8 a base of two by writing it as 2^3. Then we have 24x-3=23. Then we get rid of the base and get 4x-3=3. Finally we solve for x. 4x-3=3 4x=6 x=23 120. Explain how to solve an exponential equation when both sides cannot be written as a power of the same base. Use 3x = 140 in your explanation. To solve this equation one needs to use a natural logarithm or ln. First take the ln of both sides, ln 3x= ln 140 Then using bx= x ln b, move the variable to the front, x ln 3 = ln 140 Solve for x, x= ln3ln140= 1.0986122887/4.9416424226 = 0.22231723680404. 121. Explain the differences between solving log31x - 12 = 4 and log31x - 12 = log3 4. When solving log31x - 12 = 4 one needs to write it in the form of bc=M. To do this we do the following; logbM=c means bc=M. 1) log31x - 12 = 4 2) 34=x-12 3) 81=x-12 4) x=93 In the case of log31x - 12 = log3 4, since the log is the same on both sides of the equation the will be omitted. The new equation would be; 1x-12=4. Then solve as normal. Add 12 to 4 to get 16, leaving 1x, which is just x and you have x=16. 122. In many states, a 17% risk of a car accident with a blood alcohol concentration of 0.08 is the lowest level for charging a motorist with driving under the influence. Do you agree with the 17% risk as a cutoff percentage, or do you feel that the percentage should be lower or higher? Explain your answer. What blood alcohol concentration corresponds to what you believe is an appropriate percentage? Using the given equation to find the percentage of accident probability to alcohol level, R=6e12.77x, we can find the appropriate levels at which to operate a motor vehicle. In my family we say even if we had one drink we will not be driving. So my level will be 0.00%. Although in reality there can never be a 0% chance of an accident, so I will go with 1% chance instead of 17%, which is the acceptable rate in most states. 1) 6e12.77x=1 2) e12.77x=16 3) ln e12.77x=ln16
4) 12.77x=ln 16
5) x=ln 1612.77≈-0.14
Doing this however brings a negative result and is not possible to have a BAC of any negative amount.