Question

How do you write ${a^x} = y$ in log form?

Answer 1

Hint : The functions in which one term is raised to the power of another term are called exponential functions, in the given question, on the left-hand side, x is raised to the power of a thus it is an exponential function. The inverse of the exponential function is called logarithm function.

Complete step-by-step answer :
A logarithm function is of the form ${\log _a}b$ where a is the base and b is the term whose logarithm we are finding, the answer to ${\log _a}b$ can be defined as the power to which a should be raised to get b as the answer. So, to convert an exponential function into a logarithm function, we first identify the base and move it to the other side of the equal sign and add the term “log”. This way we can find out the correct answer.
In ${a^x} = y$ , the base of the logarithm function will be “a”, moving the base to the other side of the equal to sign and writing the word “log”, we get –
${a^x} = y \\\ \Rightarrow x = {\log _a}y \;$
Hence, ${a^x} = y$ is written in the log form as $x = {\log _a}y$ .
So, the correct answer is “ $x = {\log _a}y$ ”.

Note : The logarithm functions whose base is equal to e are called the natural logarithm functions and are denoted as $\ln a$ , they can be written in log form as ${\log _e}a$ . $e$ is an irrational and transcendental mathematical constant, its value is nearly equal to $2.718281828459$ . Certain rules are obeyed by the logarithm functions; one of those laws tells us how to convert logarithm functions to exponential functions. In the given question, we had to convert the exponential function into the logarithm function, so we used the inverse of this law.