Question

Assertion:if log2= 0.3010,then the number of digits in 16⁵⁰ is 61.
Reason:The characteristic of the logarithm of a number with the digits in its integral part is n=1.
and options are in this choose the correct option pls ans me the correct option.
1)Both A and R are true and R are is the correct explanation of A.
.2) Both A and R are true, but R is not the correct explanation of A.
3)A is true, but R is false.
4)A is false,but R is true.​

Answer 1

Answer:

Option (2)

Step-by-step explanation:

Given :-

Assertion:if log2= 0.3010,then the number of digits in 16⁵⁰ is 61.

Reason:The characteristic of the logarithm of a number with the digits in its integral part is n+1.

To find :-

Find the correct option

1)Both A and R are true and R are is the correct explanation of A.

.2) Both A and R are true, but R is not the correct explanation of A.

3)A is true, but R is false.

4)A is false,but R is true.

Solution :-

Both A and R are true, but R is not the correct explanation of A.

Check:-

Given number = 16⁵⁰

Let x = 16⁵⁰

On taking logarithms both sides then

=> log x = log 16⁵⁰

=> log x = log (2⁴)⁵⁰

=> log x = log 2²⁰⁰

=> log x = 200 log 2

Since log a^m = m log a

=> log x = 200×0.3010

=> log x = 60.2000

So The characteristic is = 60

Number of digits = Characteristic +1

=> 60+1

=> 61

Number of digits = 61

The number of digits in 16⁵⁰ is 61

Used formulae:-

→ log a^m = m log a

→ (a^m)^n = a^(mn)

→ Number of digits = Characterestic + 1

→ The integral part of a logarithm value of a number is it's characteristic.