Question

Given log(2) = 0.3010 and log(3) = 0.4771, find: log(1.5).

A) 0.1768
B) 0.3010
C) 0.3890
D) 0.4771

Answer 1

A logarithm of 1.5 is found using the given log(2) and log(3) and applying the logarithm property of quotients. The calculation yields 0.1761, which is closest to option A) 0.1768.

Step-by-step explanation:

To find log(1.5), we can utilize the property of logarithms that states the logarithm of a quotient is the difference of the logarithms (log a - log b). Since 1.5 can be expressed as 3/2, we can use the given logarithm values for 2 and 3 to find the answer.

log(1.5) = log(3/2) = log(3) - log(2)

Using the given values, log(3) = 0.4771 and log(2) = 0.3010:

log(1.5) = 0.4771 - 0.3010 = 0.1761

Therefore, the log(1.5) is approximately 0.1761, which is closest to option A) 0.1768, taking into consideration rounding differences.