"

**Exponential form**" simply means a numeric**form**involving exponents. One way to write such a number is by recognizing that each position represents a power (exponent) of 10. So you can first break it up into separate pieces.Similarly, you may ask, how do you find the exponential function?

In an

**exponential function**, the independent variable, or x-value, is the**exponent**, while the base is a constant. For example, y = 2x would be an**exponential function**. Here's what that looks like. The formula for an**exponential function**is y = abx, where a and b are constants.What is the formula for Half Life?

A

**half**-**life**usually describes the decay of discrete entities, such as radioactive atoms. Instead, the**half**-**life**is defined in terms of probability: "**Half**-**life**is the time required for exactly**half**of the entities to decay on average".1

## What is the exponential equation?

**Exponential Equations**. An

**exponential equation**is one in which a variable occurs in the exponent, for example, . When both sides of the

**equation**have the same base, the exponents on either side are equal by the property if , then .

2

## What is an example of an exponential expression?

**Exponential Expressions**. The use of an

**exponential**is a very convenient way of expressing the repeated multiplication of a number by itself. The

**exponent**is placed to the upper right of the base number and signifies how many times the base term is multiplied by itself.

3

## What is a radical exponent?

Square roots are most often written using a

**radical**sign, like this, . But there is another way to represent the taking of a root. You can use rational**exponents**instead of a**radical**. A rational**exponent**is an**exponent**that is a fraction.4

## What is exponential form in algebra?

A logarithm refers to the exponent in an

**algebraic**expression written in**exponential form**. A logarithmic expression is the inverse of an**exponential**expression. In order to convert an expression in**exponential form**to one in logarithmic**form**, you just need to fill in a, b, and c to their proper places.5

## What is the definition of exponential notation?

**Exponential notation**is a

**mathematical**method for writing longer multiplication problems in a simplified manner. This lesson will define how to work with

**exponential notation**and give some examples of how it is used. Algebra I: High School /

**Math**Courses.

6

## What is an exponential graph?

**Graphs**of

**Exponential**Functions. The

**graph**of y=2

^{x}is shown to the right. Here are some properties of the

**exponential**function when the base is greater than 1. The

**graph**passes through the point (0,1) The domain is all real numbers.

7

## What is a radical form?

Simplest

**Radical Form**. Expressing in simplest**radical form**just means simplifying a**radical**so that there are no more square roots, cube roots, 4th roots, etc left to find. It also means removing any**radicals**in the denominator of a fraction.8

## What is standard exponential notation?

A-1:

**EXPONENTIAL NOTATION**. The**exponential notation**(sometimes called the "scientific"**notation**) greatly simplifies calculations, especially with very large and very small numbers. It uses positive and negative exponents to write multiples and submultiples of 10: Any number raised to the zeroth power equals one.9

## What is a radical form of an expression?

**Radical Form**.

**Radical form**refers to a

**form**of an algebraic

**expression**in which we have a number or an

**expression**underneath a

**radical**.

10

## What is expanded exponential form?

**Expanded form**calculator shows

**expanded forms**of a number including

**expanded**notation

**form**,

**expanded**factor

**form**,

**expanded exponential form**and word

**form**. When numbers are separated into individual place values and decimal places they can also

**form**a mathematical expression.

11

## What is the logarithmic form of?

MathHelp.com. Solving

**Logarithmic**Equations. Note that the base in both the exponential**form**of the equation and the**logarithmic form**of the equation is "b", but that the x and y switch sides when you switch between the two equations.12

## How do you calculate log base 2?

If you have a

**calculator**than computes the natural**logarithm**(often denoted ln), then you can**calculate log**(x) = ln(x)/ln(_{2}**2**). The same thing works with**log base**10, i.e.**log**(x) =_{2}**log**_{10}(x)/**log**_{10}(**2**).**log**(x) means the power you have to raise_{2}**2**in order to get x. For example,**2**= 4, so^{2}**log**(4) is_{2}**2**.13

## What is the logarithm of a number?

A

**logarithm**is the power to which a**number**must be raised in order to get some other**number**(see Section 3 of this Math Review for more about exponents). For example, the base ten**logarithm**of 100 is 2, because ten raised to the power of two is 100:**log**100 = 2.14

## What is the log2?

**log2**(x) represents the logarithm of x to the base 2. Mathematically,

**log2**(x) is equivalent to log(2, x) . The logarithm to the base 2 is defined for all complex arguments x ≠ 0.

15

## Why do we use logarithms?

**Logarithms**are a convenient way to express large numbers. (The base-10

**logarithm**of a number is roughly the number of digits in that number, for example.) Slide rules work because adding and subtracting

**logarithms**is equivalent to multiplication and division. (This benefit is slightly less

**important**today.)

16

## Why do we take log?

There are two main reasons to

**use**logarithmic scales in charts and graphs. The first is to respond to skewness towards large values; i.e., cases in which one or a few points are much larger than the bulk of the data. The second is to show percent change or multiplicative factors.17

## How does a log work?

They are the same curve with x-axis and y-axis flipped. Which is another thing to show you they are inverse functions. On a calculator the Natural

**Logarithm**is the "ln" button. Always try to use Natural**Logarithms**and the Natural Exponential Function whenever possible.18

## What is log equal to?

a When you read that, you say "if a to the b power

**equals**x, then the**Log**(or**Logarithm**) to the base a of x**equals**b."**Log**is short for the word**Logarithm**. Here are a couple of examples: Since 2^3 = 8,**Log**(8) = 3. 2 For the rest of this letter we will use ^ to represent exponents - 2^3 means 2 to the third power.19

## Can you divide logs?

The rule when

**you divide**two values with the same base is to subtract the exponents. Therefore, the rule for division is to subtract the**logarithms**. The log of a quotient is the difference of the**logs**.20

## What is the formula to calculate half life?

Radioactive

**Half**-**Life Formula**. A radioactive**half**-**life**refers to the amount of time it takes for**half**of the original isotope to decay. For example, if the**half**-**life**of a 50.0 gram sample is 3 years, then in 3 years only 25 grams would remain.