Question

when a positive integer is expressed in base 7, it is , and when it is expressed in base 5, it is . what is the positive integer in decimal?

Answer 1

The question could not be answered due to missing specific information about the base 7 and base 5 representations. To convert a number from base 7 or base 5 to decimal, you would multiply each digit by its base raised to the power of its position index and add them up, but the actual base representations are required to perform this calculation.

Step-by-step explanation:

The question asks to find the positive integer that when expressed in base 7 and base 5 gives two different representations. Unfortunately, the specific base 7 and base 5 representations were not provided in the question, so we cannot complete the calculation without this information. However, to convert a number from base 7 or base 5 to decimal (base 10), you would use the following method:

1. Write down the number with its base representation.
2. For each digit, multiply it by the base raised to the power of the position of the digit, starting from 0 for the rightmost digit.
3. Add up all these values to get the number in decimal form.

For example, if a number in base 5 is 123 (in base 5), the conversion to decimal would be:

1*(5^2) + 2*(5^1) + 3*(5^0) = 25

25+ 10 + 3 = 38 in decimal form.