To convert the number (131_5) from base 5 to base 10, you multiply each digit by (5) raised to the power of its position, starting from the right (position 0). So, (1 \times 5^2 + 3 \times 5^1 + 1 \times 5^0) equals (1 \times 25 + 3 \times 5 + 1 \times 1), which simplifies to (25 + 15 + 1 = 41). Therefore, (131_5) in base 10 is (41).
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Convert the base 10 numeral to a numeral in the base indicated. 503 to base 5
In base 11 vs In base 10 10 = 11 20 = 22 30 = 33 So, it is simply dividing whatever value in base 11 by 10 then multiplying it back by 11, but digit by digit. Example, 45 in base 11: 45 = 40 + 5 (still true) = 40/10*11 + 5 (leave the 5 untouched) = 44 + 5 = 49 (in base 10)
131-126 = 5
15
log(5)125 = log(5) 5^(3) = 3log(5) 5 = 3 (1) = 3 Remember for any log base if the coefficient is the same as the base then the answer is '1' Hence log(10)10 = 1 log(a) a = 1 et.seq., You can convert the log base '5' , to log base '10' for ease of the calculator. Log(5)125 = log(10)125/log(10)5 Hence log(5)125 = log(10) 5^(3) / log(10)5 => log(5)125 = 3log(10)5 / log(10)5 Cancel down by 'log(10)5'. Hence log(5)125 = 3 NB one of the factors of 'log' is log(a) a^(n) The index number of 'n' can be moved to be a coefficient of the 'log'. Hence log(a) a^(n) = n*log(a)a Hope that helps!!!!!