The One-to-One Property of natural logarithms states that if ln x = ln y, then ________.

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Mitchel Aguirre · Accepted Answer

Step 1 Given The One to One Property of natutal logarithm states that If ln⁡x=ln⁡y, then By the Definition of one one function A f is one one If f(x)=f(y) ⇒x=y Step 2 The One to One Property of natutal logarithm states that If ln⁡x=ln⁡y then ln⁡x=ln⁡y taking exponentiation on both sie eln⁡x=eln⁡y ⇒x=y Hence, The One to One Property of natural logarithms states that f ln⁡x=ln⁡y, then x=y

star233 · Accepted Answer

Answer:If lnx=lny, it implies that x and y are equal. The One-to-One Property of natural logarithms allows us to equate the arguments of natural logarithms when their natural logarithm values are equal.Explanation:Let&#039;s first recall what the natural logarithm function, denoted as lnx, represents. The natural logarithm is the inverse function of the exponential function ex, where e is Euler&#039;s number (approximately equal to 2.71828). It tells us the exponent to which we need to raise e to obtain a given number x.Now, suppose we have two numbers x and y such that their natural logarithms are equal, i.e., lnx=lny. By the definition of equality, this means that the exponent to which we raise e to obtain x is the same as the exponent to which we raise e to obtain y. In other words, elnx=elny.Now, using the property of exponentiation, elnx=x and elny=y. Therefore, we can conclude that x=y.

alenahelenash · Accepted Answer

The One-to-One Property of natural logarithms states that if lnx=lny, then x=y.This property arises from the fact that the natural logarithm function, denoted as ln(x), is a one-to-one function, which means that it has a unique output for every input.When we have lnx=lny, it implies that the natural logarithm of both x and y is the same. Since ln(x) and ln(y) are equal, their inverses, which are x and y, must also be equal. Therefore, we can conclude that x=y.

user_27qwe · Accepted Answer

Step 1. Assume ln(x)=ln(y).Step 2. We know that the natural logarithm function, ln(x), is defined as the inverse of the exponential function ex. This means that ln(x) gives us the exponent to which we need to raise the base e to obtain x. Similarly, ln(y) gives us the exponent to which we need to raise the base e to obtain y.Step 3. Since ln(x)=ln(y), it implies that raising the base e to the power of the exponent ln(x) is equal to raising the base e to the power of the exponent ln(y). Mathematically, we can write this as eln(x)=eln(y).Step 4. According to the properties of exponents, when we raise a base to the power of another exponent, the resulting value is the base itself. Therefore, we have eln(x)=x and eln(y)=y.Step 5. Combining the above equations, we find that x=y, which proves the One-to-One Property of natural logarithms.In summary, if ln(x)=ln(y), then it follows that x=y. This property is particularly useful for solving logarithmic equations by equating the natural logarithms of different expressions and then simplifying to find the values of the variables.

The One-to-One Property of natural logarithms states that if ln x = ln y, then

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