Table of Contents

## How do you solve LN 3x?

Correct answer: According to log properties, the coefficient in front of the natural log can be rewritten as the exponent raised by the quantity inside the log. Notice that natural log has a base of . This means that **raising the log by base will eliminate both the and the natural log.**

## How do you solve for LOG LN?

**Quotient Rule**

- ln(x/y) ln(x) – ln(y)
- The natural log of the division of x and y is the difference of the ln of x and ln of y.
- Example: ln(7/4) ln(7) – ln(4)

## How do you solve LN expressions?

ln and e **cancel each other out. Simplify the left by writing as one logarithm. Put in the base e on both sides. Take the logarithm of both sides.**

## How do you find the log of ln?

**If you need to convert between logarithms and natural logs, use the following two equations:**

- log10(x) ln(x) / ln(10)
- ln(x) log10(x) / log10(e)

## How do you get rid of a log with LN?

To rid an equation of logarithms, **raise both sides to the same exponent as the base of the logarithms. In equations with mixed terms, collect all the logarithms on one side and simplify first.**

## Can you take the LN of a log?

The logarithms and exponentials cancel each other out (equation (4)), giving our product rule for logarithms, **ln(xy)ln(x)+ln(y).**