What is the difference between F (x) = lnx2 and G (x) = 2lnx? Why are they not the same function?

In the former, X is not equal to 0, while in the latter, X is greater than 0
In the image, the image of the latter is the right part of the Y-axis of the former

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1. Let f (x) = LNX, G (x) = f (x) + F '(x) 1) Finding the monotone interval and minimum of G (x) 2) Discuss the size of G (x) and G (1 / x) 3) Find the value range of a so that G (a) - G (x) 0 holds
2. Let f (x) = LNX, G (x) = f (x) + F '(x). (I) find the monotone interval and minimum value of G (x); (II) discuss the size relationship between G (x) and G (LX); (III) find the value range of a, so that G (a) - G (x) < 1A holds for any x > 0
3. Seeking indefinite integral ∫ (LNX) ^ 3 / x ^ 2 ∫(lnx)^3/x^2 dx
4. It is proved that the area of the triangle formed by the tangent line at a point on the curve f (x) = 1 / x, the line x = 0 and the line y = x is a fixed value, and And calculate the fixed value
5. The derivative of e to the power xn (n belongs to R) What's the derivative of (e ^ xn)
6. The derivative of y = x to 3 / 4 power and the derivative of y = x to 5 / 2 power than x to 1 / 3 power The derivative of y = x to 3 / 4 power and the derivative of y = x to 5 / 2 power than x to 1 / 3 power
7. Xn = y, the derivative is NX (n-1). If x = 10, then his derivative is 1 × 10 to the power of zero, which is one, not zero. What's the matter
8. It is known that the second power of X is equal to five, the square of the third power of negative two x minus three times (the third power of negative four x n)
9. Factorization factor of 3 * a * xn + 1 power-6 * a square * xn power + 3 * a cube * XN-1 power
10. Find the tangent equation of the quadratic curve y equal to x where x equals 1
11. Is f (x) = LnX3 and G (x) = 3lnx the same function? Is lnx2 and 2lnx the same function? Why?
12. Is f (x) = lnx2, G (x) 2lnx the same and why?
13. What is LNX = - 3 / 2 x
14. Why is ∫ (LNX) ^ 2 D (LNX) equal to 1 / 3 (LNX) ^ 3 Do you have any properties? Or do you continue to use the partial integration method?
15. LNX equals 1 / 3
16. LNX ^ 3 =? How much is this?
17. Why is LNX + 1 = 0 equal to 1 / E? How did he get it? So please help me to analyze it! Thanks a lot! LNX + 1 = 0, why x is - 1 / E, and how it is obtained, so please help me to analyze it! Thanks a lot!
18. -E ^ (- LNX) is equal to?
19. Is e ^ - LNX equal to - X or 1 / x?
20. LNX equals one, x equals how much