Question

Given log34≈1.2619 and log36≈1.6309, what is log3(0.5)? enter your answer in the box.

Answer 1

To find log3(0.5), use the properties of logarithms. Rewrite log3(0.5) as log3(1/2) and use the property log(a/b) = log(a) - log(b). Use the given approximations to find log3(0.5) ≈ 0 - 1.2619.

Step-by-step explanation:

To find log3(0.5), we need to use the properties of logarithms. We know that log3(4) is approximately 1.2619 and log3(6) is approximately 1.6309.

Since 0.5 = 1/2, we can rewrite log3(0.5) as log3(1/2). Using the property log(a/b) = log(a) - log(b), we can rewrite this as log3(1) - log3(2).

Since log3(1) = 0, we have log3(0.5) = 0 - log3(2).

Using the given approximations, we have log3(0.5) ≈ 0 - 1.2619.

Answer 2

To calculate log3(0.5), we rewrite 0.5 as 1/2, use the properties of logarithms and known values to find -log3(2), which is approximately -0.63095.

Step-by-step explanation:

To find log3(0.5), we can use the property of logarithms that states loga(b/c) = logab - logac. The property applies for any base, including base 3. First, notice that 0.5 can be written as 1/2. Therefore, log3(0.5) is the same as log3(1/2), which is log31 - log32.

Since log31 is 0 (because any log base of 1 is 0), what we need to find is -log32. But we were not given log32; we have log34 and log36 instead. We can use the fact that 4 is 22 and express log34 as 2*log32. From the information given, log34 is approximately 1.2619, so log32 is approximately 1.2619 / 2 ≈ 0.63095.

Therefore, log3(0.5) or -log32 is approximately -0.63095.