Solution
1. Explain why log_a1=0.
For this case because the only way to obtain 0 is when
[tex]a^0=1[/tex]2. Explain why log_a a^x=x is true if the base of the logarithm and the base used in the interior exponential function are identical.
For this case we can do the following:
[tex]\log _a(a^x)=x\log _a(a)=x\cdot1=x[/tex]3. In this unit, we explored several exponential and logarithmic models. Pick a situation related to YOUR MAJOR that would be modeled by one of the 5 models we discussed in class. Describe why this model would be helpful.
Case 1: Model to reduce the scale a given number in the base 10
[tex]\log _{10}(100)=10[/tex]Case 2: Model to find the half life of an element
[tex]T=\frac{\log _e(x)}{rate}[/tex]This model would be helpful since we can find where the middle of an initial amount is reached after some time
