# What is the properties of exponential and logarithmic functions?

## What is the properties of exponential and logarithmic functions?

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay.

Are exponential and logarithmic functions are one-to-one?

Explanation: Considering the natural logarithm, it is the inverse of the exponential function ex:R→(0,∞) , which is strictly monotonically increasing, so ln:(0,∞)→R is itself strictly monotonically increasing and one to one.

### What are the properties of logarithmic function?

Properties of Logarithms

• logb1=0 log b 1 = 0 . This follows from the fact that b0=1 b 0 = 1 .
• logbb=1 log b b = 1 . This follows from the fact that b1=b b 1 = b .
• logbbx=x log b b x = x . This can be generalized out to logbbf(x)=f(x) log b b f ( x ) = f ( x ) .
• blogbx=x b log b x = x .

What are the properties of exponential functions?

Exponential Function Properties

• The graph passes through the point (0,1).
• The domain is all real numbers.
• The range is y>0.
• The graph is increasing.
• The graph is asymptotic to the x-axis as x approaches negative infinity.
• The graph increases without bound as x approaches positive infinity.
• The graph is continuous.

## What is an exponential property?

Exponential Properties: Product of like bases: To multiply powers with the same base, add the exponents and keep the common base. 2. Quotient of like bases: To divide powers with the same base, subtract the exponents and keep the common base.

Are exponential functions one to one functions?

Exponential functions have a one-to-one property which means each input, x, value gives one unique output, y, value. Each x gives only one y, and each y gives only one x. This means exponential equations have only one solution.

### Is exponential function is one one or onto?

So yes, exponential functions are one to one.

What is one to one property of an exponential function?

Method 1: One-to-One Property. Exponential functions have a one-to-one property which means each input, x, value gives one unique output, y, value. Each x gives only one y, and each y gives only one x. This means exponential equations have only one solution.

## When can the One to One property of logarithms not be used to solve an equation?

The one-to-one property cannot be used when each side of the equation cannot be rewritten as a single logarithm with the same base.

What are exponential properties?

### What are the rules of logarithm?

The rules apply for any logarithm logbx, except that you have to replace any occurence of e with the new base b. The natural log was defined by equations (1) and (2)….Basic rules for logarithms.

Rule or special case Formula
Quotient ln(x/y)=ln(x)−ln(y)
Log of power ln(xy)=yln(x)
Log of e ln(e)=1
Log of one ln(1)=0

What are the two properties of exponents?

Exponent properties review

Property Example
( x n ) m = x n ⋅ m \left(x^n\right)^m=x^{n\cdot m} (xn)m=xn⋅m ( 5 4 ) 3 = 5 12 \left(5^4\right)^3=5^{12} (54)3=512
( x ⋅ y ) n = x n ⋅ y n (x\cdot y)^n=x^n\cdot y^n (x⋅y)n=xn⋅yn ( 3 ⋅ 5 ) 7 = 3 7 ⋅ 5 7 (3\cdot 5)^7=3^7\cdot 5^7 (3⋅5)7=37⋅57

## What are the properties of exponential equations?

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by . To solve exponential equations with same base, use the property of equality of exponential functions . If b is a positive number other than 1 , then bx=by if and only if x=y .

What is a one one function?

One to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets. It is also written as 1-1. In terms of function, it is stated as if f(x) = f(y) implies x = y, then f is one to one.

### When can the one-to-one property of logarithms be used to solve an equation when can it not be used?

When can it not be used? The one-to-one property can be used if both sides of the equation can be rewritten as a single logarithm with the same base. If so, the arguments can be set equal to each other, and the resulting equation can be solved algebraically.

Are exponential functions not one-to-one?

1 Answer. George C. Apart from such normal cases, exponential functions are often not one-one.