Was the only purpose of the $\log$ function to express the inverse of the exponential function in function form?

Question

Note: My $2$ main questions are in bold.

Why essentially was the $\log$ function was created? To answer this question, I asked myself, what would be the inverse of the function $y=2^x$. The inverse would be $x=2^y$, but why was $\log$ used for isolation of the variable $y$? Was the initial sole purpose of the $\log$ function to express such an equation in in function form?

For instance, with the equation $x=2^y$, why couldn't people just find $f(2)$ as $2=2^y$, and thus figure out the value of $f(1)=1$? Why did they need to create a whole new $\log$ function to express this in terms of $y$, when finding a table of values was just as easy, or even easier than creating a whole new function?

If there were any purposes of the $\log$ function that could not be achieved with normal exponents, what were they?

Answer 1

Logarithm was invented around 1600 by John Napier to simplify difficult calculations: a multiplication can be reduced to addition.

It was very useful in the computation of astronomical tables.

See the quote from Laplace, who called logarithms

"[a]n admirable artifice which, by reducing to a few days the labour of many months, doubles the life of the astronomer, and spares him the errors and disgust inseparable from long calculations."

Answer 2

While the logarithmic function is obviously the inverse of the exponential function it's main purpose is to convert large numbers to smaller numbers.

For example for $$x=100,000,000,$$

$$ log(x)= 8.$$

From $$log(xy)=log (x) + log (y)$$ we get $$log(3600) = 2+log(36)=2+2(log2 +log3)$$ Applications such as Earthquake Richter's scale or Radioactive half life makes logarithms a good tool to be around.

Logarithmic differentiation is used to find derivative of functions such as $$f(x)= x^x$$ and$$ f(x) = x^{sin x}.$$