Why is ln (LNX power of x) equal to (LNX power)?

Why is ln (LNX power of x) equal to (LNX power)?

This is based on the property of logarithm: Logan ^ m = mlogan
So, ln (x ^ LNX) = lnxlnx = (LNX) ^ 2
I hope you can understand it

Finding the inverse function of y = - arctan (2x-1)

y=-arctan(2x-1)
tany=-(2x-1)
tany=1-2x
x=1/2(1-tany)
The inverse of changing sign is
y=1/2(1-tanx)

Inverse function of y = pi / 2 + arctan 2x

-π/2

The inverse function of y = √ (3-x) + arctan 1 / X and y = e ^ 1 / X

The inverse function of y = e ^ (1 / x) is y = 1 / (LNX) x > 0

What is the inverse function of y = arctan √ x?

Find the range first
So 0 ≤ y < π / 2
y=arctan√x
tany=√x
x=tan²y
That is y = Tan ^ 2 (x) (0 ≤ x < π / 2)

How to find the inverse function of y = 2x + 3

y=2X+3
2x=y-3
x=(y-3)/2
The inverse function of y = 2x + 3 is x = (Y-3) / 2

Why is the inverse function of y = 2x-e ^ x y '= 2-e ^ x

This is derivative
(2x)'=2
(e^x)'=e^x
So y '= 2-e ^ x

The inverse of the function y = 2x + 1 is______ ．

∵ y = 2x + 1 ∵ x + 1 = log2y, that is, x = log2y-1, so the inverse function of function y = 2x + 1 is y = log2x-1, so the answer is: y = log2x-1 (x > 0)

It is known that f (x) is an odd function defined on R. when x > 0, f (x) = x ^ 2 + 2 ^ X. if f (2-A ^ 2) > F (a), then the value range of real number a is

F (x) is an odd function defined on R
When x > 0, f (x) = x ^ 2 + 2 ^ X
It's an increasing function
F (x) is an increasing function on R
f（2-a^2）>f（a）
∴2-a^2>a
a^2+a-2

Given the function f (x) = 3sinxcosx + cos2x − 12, X ∈ R (1) find the minimum positive period and monotone increasing interval of function f (x); (2) draw the image of function in one period

(1) This is the case that we want to get the result of the 3-sinx cosx x + cos2x x x = 12 = 32sin2x + 12cos2x = sin (2x + π 6) the minimum positive period is 2 π 2 = 2 π 2 = π. Let − π 2 + 2K π 2 + 2K + cos2x + cos2x + cos2x2x x = 12 = 32sin2x + 12cos2x + 12cos2x2x2x = 2x = sin (2x + π + π 6) 572x2x2x2x2x + 12cos2x2x2x + 12cos2x2x2x2x + 12cos2x2x2x = 2x + 12cos2x2x = 2x = 2x (2x + 12cos2x = 2x + 12cos2x + 122x + 12cos2x x + 122x = 2x + 122x = 2x = 2x = 2x& nbsp; & nbsp; & nbsp; & nbsp; & nbsp;    0            π2             π          3π2           2 π x − π 12 π 6 5 π 12 2 π 3 11 π 12 f (x) 0 10 - 10 draw an image as shown in the figure: