Practice problem
Define the following function for x>0x\gt 0x>0: f(x)=∫1xdtt.f(x) = \int_{1}^{x}\frac{dt}{t}.f(x)=∫1xtdt. Which of the following is true?
Hint
f(ab)=f(a)+f(b)f(ab) = f(a) + f(b)f(ab)=f(a)+f(b) for all a,b>0a, b\gt 0a,b>0.
f(a+b)=f(a)+f(b)f(a+b) = f(a) + f(b)f(a+b)=f(a)+f(b) for all a,b>0a, b\gt 0a,b>0.
f(ab)=f(a)×f(b)f(ab) = f(a) \times f(b)f(ab)=f(a)×f(b) for all a,b>0a, b\gt 0a,b>0.
f(a+b)=f(a)×f(b)f(a+b) = f(a) \times f(b)f(a+b)=f(a)×f(b) for all a,b>0a, b\gt 0a,b>0.
Type a concept, like “slope” or “photosynthesis”.