Final answer:
The expression log3 100 - log3 18 - log3 50 can be reduced to log3(1/9), which simplifies to -2 using the properties of logarithms since 1/9 is 3^-2.
Step-by-step explanation:
To evaluate the expression log3 100 - log3 18 - log3 50, we use the properties of logarithms. One important property is that loga(bc) = logab + logac, and similarly, loga(b/c) = logab - logac. This property applies for any base, not just base 10 or e (natural logarithms), and allows us to combine or break apart logarithmic terms.
To evaluate log3100 - log318 - log350, we can use the property of logarithms that states log(a) - log(b) = log(a/b). So, we have log3(100/18/50). Simplifying this, we get log3(5/3). Finally, evaluating this logarithm, we find that log3(5/3) = 1.
Applying this property, we can rewrite the expression as:
log3(100/18/50)
Next, we calculate the value inside the logarithm:
100/18/50 = 100/(18*50) = 100/900 = 1/9
So the expression simplifies to log3(1/9).
Since 1/9 is 3-2, we can write:
log3(3-2) = -2
Therefore, the value of the original expression is -2.