Question

Show why the quotient property and power property are true.Quotient property:log_a(u)-log_a(v)=log_a(u/v)Power property:log_a(u)^n=nlog_a(u)Follow up questions:1. Explain why log_a1=0.2. 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.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.

Answer 1

1. Explain why log_a1=0.

For this case because the only way to obtain 0 is when

`a^0=1`

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:

`\log _a(a^x)=x\log _a(a)=x\cdot1=x`

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

`\log _(10)(100)=10`

Case 2: Model to find the half life of an element

`T=(\log _e(x))/(rate)`

This model would be helpful since we can find where the middle of an initial amount is reached after some time