By definition, pH=-log_(10)[H_3O^+]
And thus, here, pH=-log_(10)(10^(-10))=-(-10)=10.
Given the definition of the logarithmic function, log_ab=c, c is that power to which we raise the base a to get b, then log_(10)10^x=x. Logs were introduced in the days BEFORE the advent of cheap electronic calculators; scientists, and economists, and engineers, and A level students, used to use "log tables", and "slide rules" which made complex calculations a bit less tiresome.
In water, under standard conditions, we can show that pH+pOH=14. What is [HO^-] in the given example?
The use of pH and pOH allows the use of buffer solutions to moderate acidity and alkalinity.
