If log 64 = 1.8061, then the value of log 16 will be (approx)?
Answers
Answer:
1.2040
Step-by-step explanation:
64= 2 ^ 6
log (64)= 1.8061
log(2^6)=1.8061
6* log (2)=1.8061
log (2)= 1.8061/ 6 ------ (i)
16=2^4
log (16)= log (2^4)
4* log (2)= (1.8061 * 4)/6 ------(ii) {From (i)}
=1.2040
Hence, log(16)=1.2040
Given : Value of log 64 is 1.8061
To find : The value of log 16
Solution :
We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of log 16)
Here, we will be using general formula of logarithm.
So,
log 64 = 1.8061
log (4)³ = 1.8061
3 × log 4 = 1.8061
log 4 = 1.8061 ÷ 3
log 4 = 0.0602
2 × log 4 = 2 × 0.0602
log (4)² = 0.1204 (approx.)
log 16 = 0.1204
(This will be considered as the final result of the given mathematical problem.)
Used formula :
- log xⁿ = n × log x
Hence, the approximate value of log 16 is 0.1204