Question

log3=0.4771 find the number digits
in 3^11
​

Answer 1

Answer:

log3=0.4771

then 3^11=0.4771^11=5.2481

Step-by-step explanation:

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Answer 2

Given,

$\[\log 3 = 0.4771\]$

Solution,

Consider the digit is x.

$\[x = {3^{11}}\]$

Taking log on both side,

$\[\begin{array}{l}\log x = \log {3^{11}}\\ \Rightarrow \log x = 11 \times \log 3\\ \Rightarrow \log x = 11 \times 0.4771\\ \Rightarrow \log x = 5.2481\end{array}\]$

The characteristics is 5.

Number of digit,

$\[\begin{array}{l} = 5 + 1\\ = 6\end{array}\]$

Hence the number of digits in $\[{3^{11}}\]$ is 6.