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

I thought I answered this exact question yesterday.

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) WRONG; the log of a product is the sum of the logs of the individual 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)  y values are all one half of those of the graph of ln x but rate of growth of each is the same

B. f(x) = 5 ln(x)  here's the faster growing graph!

C. f(x) = ln(5x)  = ln 5 + ln x; same rate of increase as ln x