Question

if log to the base 10 is equal to 0.3010 3 to the base 10 is equals to zero point 4771 then find the number of digits is 36 power 6​

Answer 1

Answer:

9

Step-by-step explanation:

If the base is 10, we can simply write log₁₀2 as log 2.

Given, log 2 = 0.30103 and log 3 = 0.47712

To find the number of digits in 3¹² × 2⁸, take the log of 3¹² × 2⁸

\sf \implies log(3^{12} \times 2^8)\\\\\implies log3^{12} + log2^8 \\\\(since, log(mn) = log m + log n) \\\\\implies 12 log (3) + 8log(2)\\\\(since, log a^N = N \times log(a)) \\\\\implies 12 \times 0.47712 + 8 \times 0.30103 \\\\\implies 5.72544 + 2.40804\\\\\implies 8.13368\\

Here, we got the outcome as 8.13368. The decimal part is known as mantissa and the integral part is characterisitic (that is 8 here). To find the number of digits, add 1 in characteristic.

hence, answer is 8 + 1 = 9