Question

Сравните log0.5 3 и sin3

Answer 1

log0.5 3 = ( log3 3 ) / ( log3 0.5 ) = 1 / ( log3 0.5 )

log3 0.5 < 0

log0.5 3 = 1 / ( log3 0.5 ) < 0

sin3 > 0

log0.5 3 < sin3

Answer 2

To compare the values of log base 0.5 of 3 and sin(3), we'll need to calculate each of them:

1. log0.5(3): The expression log0.5(3) represents the logarithm of 3 to the base 0.5. We can calculate it as follows:

log0.5(3) = log(3) / log(0.5)

Using a calculator, we find: log(3) ≈ 0.4771 log(0.5) ≈ -0.3010

So, log0.5(3) ≈ 0.4771 / -0.3010 ≈ -1.585

2. sin(3): The expression sin(3) represents the sine of the angle 3 radians. Again, using a calculator:

sin(3) ≈ 0.1411

Now, let's compare the values:

log0.5(3) ≈ -1.585 sin(3) ≈ 0.1411

Since -1.585 is less than 0.1411, we can conclude that:

log0.5(3) < sin(3)