Evaluate:
Log243/120-log54/75+log24/27-log5/2
what is
log (243*24*75*2/120*54*27*5)=
log (1)=
0
or, it is
5log3 - (3log2 + log3 + log5) - (log2 + 3log3) + (log3 + 2log5) + (3log2 + log3) - 3log3 - log5 + log2 = 0
To evaluate the given expression: Log243/120-log54/75+log24/27-log5/2, we can simplify each logarithm individually and then perform the subtraction.
Let's start by simplifying each logarithm:
1. Log243/120:
To evaluate log243/120, we can use the logarithmic properties. Recall that log(A/B) is equivalent to log(A) - log(B).
So, log243/120 = log(243) - log(120).
2. Log54/75:
Using the same property, log54/75 = log(54) - log(75).
3. Log24/27:
Similarly, log24/27 = log(24) - log(27).
4. Log5/2:
Once again, applying the property, log5/2 = log(5) - log(2).
Now, substituting these simplified logarithms back into the original expression, we have:
(log(243) - log(120)) - (log(54) - log(75)) + (log(24) - log(27)) - (log(5) - log(2)).
Next, we can use properties of logarithms to combine the terms:
log(243) - log(120) - log(54) + log(75) + log(24) - log(27) - log(5) + log(2).
Finally, we can apply the subtraction of logarithms:
log(243) + log(75) + log(24) + log(2) - log(120) - log(54) - log(27) - log(5).
Now, we can use a calculator or logarithmic tables to find the decimal approximation of each logarithm and then add or subtract accordingly to obtain the final value.