Question

Find the number of digits in 3^12 x 2^18, having given
log 2 = 0-301030 and log 3 = 0.4771213.

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

\begin{gathered}\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\\\end{gathered}⟹ log(312×28)⟹log312+log28(since,log(mn)=logm+logn)⟹12log(3)+8log(2)(since,logaN=N×log(a))⟹12×0.47712+8×0.30103⟹5.72544+2.40804⟹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

\rule{200}2

Hope you understand

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