# Write as the sum and or difference of logs Intuitively, the question is: How long do I wait to get 1x my current amount? The log of a sum is NOT the sum of the logs.

### Write as the sum and or difference of logs

Sure, we could just use ln 9. That is, they've given me one log with a complicated argument, and they want me to convert this to many logs, each with a simple argument. The log of a product is the sum of the logs. This leads to all sorts of useful rules of thumb, like that a pH change of 0. Circle that 8. What is the power of 10 that gives you 1? They follow from the rule quite simply, but in general if you have a calculator you don't really need them for practical problems. In this case, I have a "2x" inside the log. Expand log5 x3. Intuitively, the question is: How long do I wait to get 1x my current amount?

Rephrase this: What happens to powers of 10 when you multiply numbers together? E is About Growth The number e is about continuous growth. With me?

## Express the following as a sum difference or multiple of logarithms

Ok, how about the natural log of a negative number? Division into subtraction? The quotient of the logs is from the change of base formula. Logs to base "e" crop up a great deal when people derive equations from fundamental physics. NB it is actually quite useful to remember that log 2 is almost exactly 0. These are true for either base. Following, is an interesting problem which ties the quadratic formula, logarithms, and exponents together very neatly.

Read more about e. The natural log gives us the time needed to hit our desired growth. This leads to all sorts of useful rules of thumb, like that a pH change of 0. However, The log of a product is the sum of the logs The sum of the logs is the log of the products The log of a quotient is the difference of the logs The difference of the logs is the log of the quotient The exponent on the argument is the coefficient of the log The coefficient of the log is the exponent on the argument Okay, so the last two aren't so melodic.

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