Properties of Logarithms Conversion

How can Wendy convert the equation f(x) = 2x to a logarithmic function when strength is 625 Pascals?

Final answer: The correct conversion of the exponential function f(x) = 2x to a logarithmic function with a strength of 625 Pascals is A) log₂(625) = x.

To convert the equation f(x) = 2x to a logarithmic function when the strength is 625 Pascals, we need to apply the properties of logarithms. Logarithms are the inverse operations of exponentiation and can help us rewrite exponential equations in logarithmic form.

The properties of logarithms state that the logarithm of a number raised to an exponent is equal to the exponent times the logarithm of the number. Additionally, the logarithm of a product is equal to the sum of the logarithms of the individual numbers.

Given the exponential function f(x) = 2x, we first rewrite it as 2^x = 625. To convert this exponential function to a logarithmic function, we find that log₂(625) = x is the correct conversion.

Therefore, the correct choice is A) log₂(625) = x, as it accurately represents the conversion of the equation f(x) = 2x to a logarithmic function when the strength is 625 Pascals.

It's important to understand the fundamental properties of logarithms to effectively convert between exponential and logarithmic functions. This knowledge is essential for solving complex equations and understanding the relationship between exponents and logarithms. By mastering logarithmic conversions, you can enhance your problem-solving skills and tackle logarithmic functions with confidence.