Suppose you are told that log(2)=0.3562 and log(3)=0.5646. All of them with the base of 'a'. Find:
i) log(6)
ii) log(9)
Solutions
i) log(6)= log (3)(2)
= log 3 + log 2
= 0.5646 + 0.3562
= 0.9208
ii)log(9)= log 3^2
= 2 log 3
= 2 (0.5646)
= 1.1292
you are correct.
An interesting question now would be ...
what is the value of 'a' ?
To find the values of log(6) and log(9) using the given information, you need to understand the properties of logarithms.
i) To find log(6), you can use the property that log(a * b) = log(a) + log(b). In this case, you have log(6) = log(3 * 2). Using the given values of log(2) and log(3), you can add them together to find log(6).
log(6) = log(3) + log(2) = 0.5646 + 0.3562 = 0.9208.
ii) To find log(9), you can use the property that log(a^b) = b * log(a). In this case, you have log(9) = log(3^2). Using the given value of log(3), you can multiply it by 2 to find log(9).
log(9) = 2 * log(3) = 2 * 0.5646 = 1.1292.