The known equation LG (x-1) + LG (3-x) = LG (A-X) (1) If the equation has and only one root, find the value range of A (2) If the equation has no real root, find the value range of A Please write down the specific problem-solving process The problem is that there is only one root, not that two are equal~

What if the function itself is meaningless? It should be classified and discussed

What is the relationship between exponential function and logarithmic function?

In elementary mathematics, we can not understand the convenience of turning logarithms into exponents, such as y = 2 ^ x = e ^ (LN2 ^ x) =

Relationship between exponential function and logarithmic function Shouldn't y = a ^ X and x = log (a) y be inverse functions So why can y and X be swapped? Textbooks say it's habit But isn't the exchange the same Please explain why I've been spending a lot of time on this

Y = a ^ x should not be inverse function with x = log (a) y. that is, X in exponential function is y in logarithmic function
Y and X are interchangeable
When we deduce y = log (a) x from y = a ^ x, we can calculate y = a ^ X by taking logarithms on both sides at the same time. After calculating x = log (a) y, we can change the position of Y and X, Let y be the dependent variable on the left side of the equal sign, and X on the right side of the equal sign. Finally, wait until y = log (a) X

On the relationship between exponential function and logarithmic function The inverse function of the function y = e to the power of 2x is? The answer is y = 1 / 2lnx (x > 0) How do I calculate y = ln (2x) (x > 0) I hope high school students who love learning and learn well can communicate with me 526970969

y=e^2x,
Let, e ^ 2x = m, have
LNM = 2x, x = (1 / 2) * LNM, and y = m, so, there are
Y = (1 / 2) LNX

Please consult the conversion of logarithmic function and exponential function How to find the value of y = BX, B from LNY = alnx (a is a constant)?

lny=alnx
Take the exponent e on both sides to get:
y=x^a
bx=x^a
b = x^(a - 1）

What is the difference between exponential function and logarithmic function

They are inverse functions, the exponential function y = a ^ x (a > 0 and a ≠ 1) (x ∈ R) and the logarithmic function y = log (a) x (a > 0 and a ≠ 1)

What is the difference between logarithmic function and exponential function?

The exponential function is f (x) = a ^ x (a > 0 and a is not equal to 1) Note: the independent variable of the exponential function must be x, and the coefficient must be 1. For example, f (x) = a ^ (x + 1) f (x) = 2A ^ X are not exponential functions. These are called exponential functions, which means that the form is like an exponential function but not an exponential function

Exponential function logarithmic function Given the function y = in X, X ∈ (0,1], { If the x power of E, the image of X ∈ (1, + ∞) and the image of function y = f (x) are symmetric with respect to the straight line y = x, then the definition domain of y = f (x) is_________

The image and the image of the function y = f (x) are symmetric with respect to the line y = X
It is shown that the relationship between them is function and inverse function
Therefore, the defined domain is the value domain of the original function
Y = in X, X ∈ (0,1], the range is: (- ∞, 0]
Y = e to the power of X, X ∈ (1, + ∞), the range is: (E, + ∞)
Therefore, the defined domain is as follows:
(-∞,0] U (e,+∞）

The problem of exponential function and logarithmic function When the base number is less than 1 and greater than 0, does the exponent under the same base number have y = x? What is the coordinate Does monotonically increasing even function exist

When the base number a ∈ (0,1), the exponential function and the logarithmic function have intersection points, because they are inverse functions of each other, so the intersection point must be on the straight line y = X. (see Figure)
However, it is more difficult to find the coordinates of the intersection point. It is necessary to solve the equation a ^ x = X
For example, to solve 0.5 ^ x = x,
(1) Let x = 1, calculate 0.5 ^ x, get 0.5;
(2) Let x = 0.5, calculate 0.5 ^ x, get 0.707;
(3) Let x = 0.707 and calculate 0.5 ^ x to obtain 0.613;
……
If the previous calculation result is set as X and substituted with 0.5 ^ x, the final conclusion will tend to be 0.641186 of the equation
In addition, the monotonically increasing even function is f (x) = 0. Of course, it is not strictly monotone increasing, and the strictly monotone increasing even function does not exist
Definition of increasing function: in the definition domain, if x 1 < x 2 satisfies f (x 1) < = f (x 2), then this function is an increasing function
If it is strictly increased, the above < = is changed to <

30 degrees, 45 degrees, 105 degrees. What triangle is this

It's an obtuse triangle