Question

Does your calculation use the fact that ln is continuous? 4. (a) Find a base b such that log_b x = 3 ln x. Explain why your b makes sense, thinking in terms of exponents. (b) Find d/dx(log_3 x / log_7 x). Fully simplify your answer, and explain why it had to be what you got. (c) Is a similar thing true for d/dx(3^x / 7^x)? Why or why not?

          Does your calculation use the fact that ln is continuous?
4. (a) Find a base b such that log_b x = 3 ln x. Explain why your b makes sense, thinking in terms of exponents.
(b) Find d/dx(log_3 x / log_7 x). Fully simplify your answer, and explain why it had to be what you got.
(c) Is a similar thing true for d/dx(3^x / 7^x)? Why or why not?