word problem

Question

Please answer the following 2 questions:
1. Identify the equation(s) that are wrong. Explain any incorrect ones; provide complete details.

A. log 6(m + n) = log 6 • log (m + n)

B. log 10 = 1

C. log m/log n = log(m/n)

2. Compared to f(x) = ln(x), which of the following increases faster? Justify your decision; answer in a complete sentence.

A. f(x) = 0.5 ln(x)

B. f(x) = 5 ln(x)

C. f(x) = ln(5x)

Answer 1

1)

 

For A, log6 is not distributed correctly.  For B, the property of subtracting logs when dividing the log's arguments is not use correctly.

 

 

1)

 

Vertical stretches always increase faster than horizontal stretches.  Choice C represents a horizontal stretch because the input is being multiplied.  So we look for the highest coefficient of f(x).  Choice B has faster increase.

Answer 2

Part 1.
A. log 6(m + n) = log 6 • log (m + n)   WRONG; justify by taking log of the product as SUM of logs of its factors.

B. log 10 = 1

C. log m/log n = log(m/n)   WRONG

 

2. Compared to f(x) = ln(x), which of the following increases faster? Justify your decision; answer in a complete sentence.

A. f(x) = 0.5 ln(x)

B. f(x) = 5 ln(x)  THIS IS THE ONE THAT INCREASES FASTER

C. f(x) = ln(5x)