How do you solve the equation log(x) = y for x?

How do you solve the equation log(x) = y for x?

• A. x = 10^y
• B. x = y^10
• C. x = e^y
• D. x = log(y)

Answer: (A)

To solve the equation log(x) = y for x, we utilize the properties of logarithms. The expression log(x) typically refers to the common logarithm (base 10), although it can also be base e (natural logarithm), depending on context. If we treat it as base 10, we can rewrite the equation in exponential form. Starting with log(x) = y, we translate this into its exponential form, which states that x is equal to 10 raised to the power of y. Hence, x = 10^y. This relationship is fundamental in logarithmic functions, where the logarithm represents the power to which the base must be raised to obtain a given number. Understanding this transformation is crucial in solving logarithmic equations, as it allows for the conversion between logarithmic and exponential forms, making it easier to isolate the variable in question. The other options involve operations that do not align with the properties of logarithms or the relationships established by the logarithmic and exponential functions, which is why they do not provide the correct solution to the given equation.

To solve the equation log(x) = y for x, we utilize the properties of logarithms. The expression log(x) typically refers to the common logarithm (base 10), although it can also be base e (natural logarithm), depending on context. If we treat it as base 10, we can rewrite the equation in exponential form.

Starting with log(x) = y, we translate this into its exponential form, which states that x is equal to 10 raised to the power of y. Hence, x = 10^y. This relationship is fundamental in logarithmic functions, where the logarithm represents the power to which the base must be raised to obtain a given number.

Understanding this transformation is crucial in solving logarithmic equations, as it allows for the conversion between logarithmic and exponential forms, making it easier to isolate the variable in question.

The other options involve operations that do not align with the properties of logarithms or the relationships established by the logarithmic and exponential functions, which is why they do not provide the correct solution to the given equation.