I don't fully get what it's saying myself (maybe if you uploaded a picture of the graphs we could help better?) but I'll try to explain a little.

“The inverse operation to exponentiation is logarithms, and as exponents aren't commutative like addition and multiplication are, there are two possible inverses, the other being surds.

\(y=2^x\) is an exponential, and you would get the inverse by placing the \(y\) where the \(x\) is.

Solving for \(y\) requires using a logarithm.

The Basic form of a logarithm

\(y=a^x \therefore \log_a {y}=x\)

Eg: \(64=2^x \quad \log_2 {64} = x, \quad x=8\)

So, when solving the aforementioned equation, we would find that the inverse function to \(y=2^x\) is \(y=\log_2 {x}\).

We can visually see that this is correct when we graph it, by inserting the line \(y=x\), showing that the reflection is symmetrical about this line.

By commutative, the textbook is saying that unlike addition and multiplication, where \(1+2=2+1\) and \(a\times b=b\times a\), an exponential cannot be the so easily switched around...

i.e: \(2^x \ne x^2\)

Please reply if anything doesn't make sense, and I'll try to help more.

Also, Welcome to AN...