a^b x c^a = abca

[bonanova 81]

Find a, b, c.

a^b x c^a= abca , a 4-digit number

[rocdocmac 8]

Spoiler

Answer:

a = 2, b = 5, c = 9

2^5*9^2 = 2592

 

 

Edited April 5 by rocdocmac

[BMAD 63]

I hope there is a nuanced way of solving this besides brute force.

[rocdocmac 8]

 

On 4/5/2018 at 10:24 PM, BMAD said:

I hope there is a nuanced way of solving this besides brute force.

Trust so too!

BN ... is there a way to work it out mathematically? I don't think that logarithms will suffice!

[bonanova 81]

Not that I know of. Tables of powers, or spreadsheet where different abc values can be simply typed in, or inspired guesswork?
It's not my fav type of puzzle, but some like this type.

[rocdocmac 8]

Thanks!