Determine if True 2 natural log of e^( natural log of 2(75))- natural log of e^( natural log of 10(75)) = natural log of 30

Rewrite the equation in exponential form using the definition of a logarithm. If ${\displaystyle x}$ and ${\displaystyle b}$ are positive real numbers and ${\displaystyle b\ne 1}$, then ${\displaystyle y=log\left(b\right)\left(x\right)}$ is equivalent to ${\displaystyle b^y=x}$.

The left side ${\displaystyle 30}$ does not equal to the right side ${\displaystyle 0}$, which means that the given statement is false.

False