Question

1. Write the expression as a single natural logarithm; ln x - 2 ln c
2. Write the logarithmic form; 2^5=32
3. Write the equation in exponential form; log4 1/16 = 8
4. Expand the logarithmic expression; log3 d/12
5. Use natural logarithms to solve the equation. 8e^4x+8= 15

My teacher game us a review packet and the answers to it, but I want to learn how to do them. Can someone explain them to me?

Answer 1

Do you know the rules and properties for logarithms?

Here is a pretty good, concise review:
http://www.andrews.edu/~calkins/math/webtexts/numb17.htm

Answer 2

So starting with: ln x - 2 ln c

you can re-write the 2ln(c) using \(\large log_b(x^n) = n log_bx\)

This allows you to bring the coefficient out in front of the log expression "inside" the log function.

Then you'll be able to use \(\large log_b(x)-log_b(y) = log_b(x/y)\)