Exponents and order of operations

Question

Use the numbers 1,2,4 and 5 in any order to write expressions to equal each integer from 1 to 20

Answer 1

this is a tedious time consuming problem

with usually trial and error, it's also possible

for some number between 1 and 20 it's not possible

here's most all of them, except one

(2-1)^(5-4) = 1

or (5-2)/(4-1) =1

(2-1)+(5-4) = 2

(5+4)/(2+1)= 3

(5-1)/(4-3) = 4

(5/1)/(4-3) =5

(5-2)+(4+1)=6

.(5+4-2)^1 = 7

(5+1)+(4-2) = 8

(5-2)^(4-1) = 9

(5)(4)/(2)(1) = 10

(2+4+5)/1 = 11

1+2+4+5 = 12

5^1 + (2)(4) =13

(5)(2)+4(1) = 14

... =15

4^(5-2-1)=16

1^5 + 2^4=17

(5)(4) - (3-1) = 18

(5)(3) +4(1) = 19

(5)(4)/(2-1) = 20

that's 95% of them

You fill in the other missing integer, for 15

keeping in mind it may not even be possible

If not possible, it will be very time cosuming.

while it may have several solutions

or there may be a mistake somewhere in the above 19 integers

no guarantees, all around

(hint: it is possible.

another hint:

one way involves no exponents or subtraction

3rd hint: one way starts with 1 and ends with 5)