What is the inverse of the function y = log(10x) in simplest form?

What is the inverse of the function y = log(10x) in simplest form?

• A. y = 10^(x - 1)
• B. y = log(10/x)
• C. y = 10^x
• D. y = log(x)/10

Answer: (A)

To find the inverse of the function \( y = \log(10x) \), we start by rewriting the equation in terms of \( x \). The function can be expressed in exponential form as: \[ y = \log(10x) \implies 10x = 10^y \] Next, solve for \( x \): \[ x = \frac{10^y}{10} = 10^{y - 1} \] We can now express the inverse function by switching \( x \) and \( y \): \[ y = 10^{x - 1} \] This gives us the inverse function in the form of \( y = 10^{x - 1} \), which matches the answer provided. Therefore, this option is correct. The process of solving the equation to find the inverse demonstrates how logarithmic and exponential functions relate to each other and confirms the accuracy of the solution. In this case, the other options do not align with the properties necessary to derive the correct inverse for the given logarithmic function.

To find the inverse of the function ( y = \log(10x) ), we start by rewriting the equation in terms of ( x ). The function can be expressed in exponential form as:

[

y = \log(10x) \implies 10x = 10^y

]

Next, solve for ( x ):

[

x = \frac{10^y}{10} = 10^{y - 1}

]

We can now express the inverse function by switching ( x ) and ( y ):

[

y = 10^{x - 1}

]

This gives us the inverse function in the form of ( y = 10^{x - 1} ), which matches the answer provided. Therefore, this option is correct. The process of solving the equation to find the inverse demonstrates how logarithmic and exponential functions relate to each other and confirms the accuracy of the solution. In this case, the other options do not align with the properties necessary to derive the correct inverse for the given logarithmic function.