Is there a formula for logarithm? A ^ log a ^ n = n?

Is there a formula for logarithm? A ^ log a ^ n = n?

When a > 0 and a ≠ 1, n > 0, a ^ (loga n) = n is right!
The explanation is as follows:
Let loga n = T. from the interaction of logarithm and exponent, we can see that a ^ t = n
So there is: A ^ (loga n) = a ^ t = n

Given that (M-3) x m-2 = - 5 is a linear equation of one variable about X, how to find the value of M? [(M-3) x is the square of (M-3) x]

M-2 is the square of (M-3) x, not so, but m-2 is the degree of X
M - 2 = 1
|m|=3
m=±3
When m = 3, M-3 = 0, not suitable for the problem
So: M = - 3

If - 5x power of a is greater than x + 7 power of a (a > 0 and a ≠ 1), the value range of X is obtained

A^(-5X)>A^(X+7)
(a > 0 and a ≠ 1),
When 01, - 5x > x + 7 = = > x

In order to make the power 0 of (x-1) and the power 2 of (x + 1) meaningful, the value of X should satisfy the following conditions

The power of 0 is meaningless
∴x-1≠0
The condition of X is that x ≠ 1

In order to make (x-1) 0 - (x + 1) - 2 meaningful, what conditions should the value of X satisfy?

From the meaning of the question: X-1 ≠ 0, x + 1 ≠ 0, the solution: X ≠ 1 or - 1

If the image of power function f (x) passes through (2,1 / 8), then the value of F (1 / 2) is

Let f (x) = x ^ n, then 2 ^ n = 1 / 8, so n = - 3
f(1/2)=8

Satisfy the inequality - 1 ≤ x

5
0 1 2 3 4

Find the natural number satisfying the inequality X-1 / 2 ≤ 1 and X-2 < 4 (x + 1)

x-1/2≤1
x≤3/2
x-2＜4（x+1)
x-2-6
x>-2
So - 2

If the sum of four consecutive natural numbers is less than 34, how many groups of such natural numbers are there?
Come on, spicy

There's only one group
34÷4=8.5
This group is 7, 8, 9, 10

It is known that the sum of four continuous natural numbers is not more than 34. There are several groups of such natural numbers

The reason is: let the smallest of four continuous natural numbers be n, and the other three be n + 1 N + 2 N + 3
N + N + 1 + N + 2 + N + 3 less than or equal to 34
N is less than or equal to 7
So the sum of four continuous natural numbers is not more than 34, and such a natural array has 8zu