# What does expand each logarithm mean?

Asked By: Aurita Liebchen | Last Updated: 1st May, 2020
Category: science physics
4.5/5 (40 Views . 13 Votes)
Learn how to expand logarithms using product/quotient rule. And when given a logarithm expression involving the logarithm of a number raised to a certain exponent, the logarithm can be expanded by multiplying the exponent to the logarithm of the number without the exponent.

Moreover, what does it mean to expand a logarithm?

Since this radical is a square root that means the power is just ½. Just think of it as the power or exponent of ½. So this problem is reduced to expanding a log expression with a power of ½. This is where the Power Rule brings down that exponent ½ to the left of the log, and then you expand the rest as usual.

Also Know, how do you undo a log? Steps to Find the Inverse of a Logarithm

1. STEP 1: Replace the function notation f (x) by y.
2. f (x) → y.
3. STEP 2: Switch the roles of x and y.
4. STEP 3: Isolate the log expression on one side (left or right) of the equation.
5. STEP 4: Convert or transform the log equation into its equivalent exponential equation.

Also to know, what are the log rules?

Logarithm rules

Rule name Rule
Logarithm product rule logb(x ∙ y) = logb(x) + logb(y)
Logarithm quotient rule logb(x / y) = logb(x) - logb(y)
Logarithm power rule logb(x y) = y ∙ logb(x)
Logarithm base switch rule logb(c) = 1 / logc(b)

What does Ln mean?

natural logarithm

### How do you expand a square root?

Expansion of square roots involves multiplying and then simplification. Expand: First, distribute the square root of two across the parentheses: This simplification involved turning a product of radicals into one radical containing the value of the product (being 2×3 = 6).

### Is it possible for a logarithm to equal a negative number?

The only numbers you can plug into a logarithm are positive numbers not equal to 1. Negative numbers, and the number 0, aren't acceptable arguments to plug into a logarithm, but why? The reason has more to do with the base of the logarithm than with the argument of the logarithm.

### What is the property of log?

Recall that we use the product rule of exponents to combine the product of exponents by adding: xaxb=xa+b x a x b = x a + b . We have a similar property for logarithms, called the product rule for logarithms, which says that the logarithm of a product is equal to a sum of logarithms.

### How do you solve for exponents?

How to solve for exponents
1. xn=y. Take the log of both sides:
2. logxn=logy. By identity we get:
3. n⋅logx=logy. Dividing both sides by log x: n=logylogx. Find the exponent of a number.
4. 3n=81. Take the log of both sides:
5. log3n=log81. By identity we get:
6. n⋅log3=log81. Dividing both sides by log 3: n=log81log3.