What does expand each logarithm mean?

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

STEP 1: Replace the function notation f (x) by y.
f (x) → y.
STEP 2: Switch the roles of x and y.
STEP 3: Isolate the log expression on one side (left or right) of the equation.
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	log_b(x ∙ y) = log_b(x) + log_b(y)
Logarithm quotient rule	log_b(x / y) = log_b(x) - log_b(y)
Logarithm power rule	log_b(x ^y) = y ∙ log_b(x)
Logarithm base switch rule	log_b(c) = 1 / log_c(b)

What does Ln mean?

natural logarithm

24 Related Question Answers Found

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

xn=y. Take the log of both sides:
logxn=logy. By identity we get:
n⋅logx=logy. Dividing both sides by log x: n=logylogx. Find the exponent of a number.
3n=81. Take the log of both sides:
log3n=log81. By identity we get:
n⋅log3=log81. Dividing both sides by log 3: n=log81log3.