What is The Inverse of Logarithmic Function? – In mathematics, the inverse of a logarithmic function is an exponential function. A logarithmic function is a type of mathematical function that is used to represent a relationship between two variables that change at different rates. The inverse of a logarithmic function is an exponential function that “undoes” the effects of the logarithmic function.
The logarithmic function is written in the form logb(x), where b is the base of the logarithm and x is the argument of the logarithm. The inverse of this function is written as b^x, where b is the base of the logarithm and x is the exponent. This exponential function takes the place of the argument in the logarithmic function, while the base remains the same.
For example, the logarithmic function log10(x) would have an inverse of 10^x. And the logarithmic function log2(x) would have an inverse of 2^x.
One way to find the inverse of logarithmic function is by reversing the operations. If we have logbase(a) of x = b, we can solve for x by raising the base a to the power of b. which is x = ab.
It’s also important to note that not every logarithmic function has an inverse. The inverse of a logarithmic function only exists if the logarithmic function is a bijection. The logarithmic functions with base a, where a is greater than 0 and not equal to 1, are bijections, which means their inverse functions exist.
In summary, logarithmic function and exponential function are inverse of each other. The inverse of logarithmic function takes the form of exponential function. By reversing the operation, it can be solved for the original value. Also, not all logarithmic functions have inverses. It’s only the logarithmic functions with base greater than 0 and not equal to 1 that have inverses.