Arrange Mathematical Operation Using 0-9 to Match the Post Number

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Participants are tasked with arranging the digits 0-9 to create mathematical expressions that equal the post number, adhering to three specific rules: no double posting, no approximations, and no invented variables. The thread begins with an example that successfully results in the number 1 using the expression "94875326 x 0 + 1." Subsequent posts follow suit, showcasing various calculations that yield the corresponding post numbers, such as "34,567,892^0 + 1 = 2" and "0·1 + (3 - 2) + (5-4) + (7-6) + (9-8) = 4." The challenge encourages creativity and mathematical thinking while fostering engagement among participants. Overall, the thread promotes a fun and interactive way to explore mathematical operations.
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In this puzzle, you use all integers from 0 to 9 to arrange a mathematical calculation whose result is the post number. There are only three rules:
1. No double posting
2. No approximation
3. No made-up variables
Now since it is the first post here, let me do it first which results in 1:
94875326 x 0 + 1= 1
Let's the fun begin! *say it in Sakaki Yuya's style*
 
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$34,567,892^0 + 1 = 2$
 
$34,567,891^0 + 2 = 3$
 
$0\cdot 1 + (3 - 2) + (5-4) + (7-6) + (9-8) = 4$
 
$34,267,891^0 + 5 = 5$
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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