In a certain number system, the number 1234 represents the decimal number 1*8^3

In a certain number system, the number 1234 represents the decimal number 1*8^3 + 2*8^2 + 3*8^1 + 4*8^0. What is the base of this number system?

In a certain number system, the number 1234 represents the decimal number 1*8^3 + 2*8^2 + 3*8^1 + 4*8^0. What is the base of this number system?

Step 1: Identify the number given in the question, which is 1234.
Step 2: Understand that the number is expressed in a certain base system.
Step 3: Recognize that the digits in the number (1, 2, 3, 4) are multiplied by powers of the base.
Step 4: Notice that the highest digit (1) is in the 8^3 place, which means the base is likely 8.
Step 5: Confirm that the other digits (2, 3, 4) follow the same pattern with decreasing powers of 8 (8^2, 8^1, 8^0).
Step 6: Conclude that since the powers of 8 are used, the base of this number system is 8.

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