Writings In Mathematics
119. Explain how to solve an exponential equation when both sides can be written as a power of the same base.
An exponential equation in which each side can be expressed in terms of the same base can be solved using the property: If , then x=y. (where and If you can express both sides of the equation as powers of the same base, you can set the exponents equal to solve for x.
Since the bases are the same, set the exponents equal to one another:
2x + 1 = 3x - 2
3 = x
120. Explain how to solve an exponential equation when both sides cannot be written as a power of the same base.
Unfortunately, not all exponential equations can be expressed in terms of a common base. For these equations, logarithms are used to arrive at a solution using common log or natural in.
1. Isolate the exponential expression.
2. Take log or ln of both sides.
3. Solve for the variable.
121. Explain the differences between solving and
(bases are equal)
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 cut off percentage, or do you feel that the percentage should be lower or higher?
I agree to the 17% cutoff rate because it gives you a little more room to play with if your blood alcohol level reads .08. For example: 6e^(12.77(.08)) equals to about 16.6658%. If the blood concentration level was at .09 than the percentage would be close to 19%(6e^(12.77(.09))=18.958%) and that seems like a lot for the human body. My guess is just to stay with the 17% because if you give people extra slack to a limit, they will abuse it and more citizens will drive drunk.