Question

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Answer 1

$\LARGE{ \underline{ \blue{ \sf{Required \: answer:}}}}$

The value of log 2 base 10 is given, and ww have to find the no. of digits in 2¹⁰⁰⁰.

GiveN:

• $\rm{ log_{10}(2) = 0.3010}$

We have to find the value of 2¹⁰⁰⁰. Taking log to find the number of digits.

⇛ $\rm{ log_({2}^{1000}) }$

This can be written as (according to logarithmic rule):

⇛ $\rm{ 1000 \:log_{2} }$

The base 10 is invisible sometimes, but it is there. Putting the value of log 2:

⇛ $1000 \times 0.3010$

The result will be:

⇛ $301$

The characteristic is 301. So, the number of digits is 2¹⁰⁰⁰ will be 301 + 1 = 302. The correct answer is Option B.

Answer 2

Question

Number of digit in 2¹⁰⁰⁰ if log ¹⁰ 2 = 0.3010

To find

Number of digits

Answer

We have to write according to logirthm rule

1000 log 2

Now, the base of 10 is visible so it's easy

Put the value of log 2

$1000 \times 0.3010$

$\huge \sf {Result = 301}$

The characteristic is 301. So, the number of digits is 2¹⁰⁰⁰ will be 301 + 1 = 302.

$\huge \fbox {The answer is Option 'B' }$

Hope it helps