(log-16%2Blog-1-6).jpeg "(log 21-log 210)(log 16+log 1 6)")
Simplifying the Expression: (log 21 - log 210)(log 16 + log 1/6)
Introduction
In this article, we will simplify the expression (log 21 - log 210)(log 16 + log 1/6). To do this, we will use the properties of logarithms and algebraic manipulations.
Properties of Logarithms
Before we start, let's recall some important properties of logarithms:
- Logarithm of a product:
log(ab) = log(a) + log(b) - Logarithm of a quotient:
log(a/b) = log(a) - log(b) - Logarithm of a reciprocal:
log(1/a) = -log(a)
Simplifying the Expression
Let's break down the expression into two parts:
Part 1: (log 21 - log 210)
Using the property of logarithm of a quotient, we can rewrite the expression as:
log(21/210)
Simplifying further, we get:
log(1/10)
Now, using the property of logarithm of a reciprocal, we get:
-log(10)
Part 2: (log 16 + log 1/6)
Using the property of logarithm of a product, we can rewrite the expression as:
log(16/(1/6))
Simplifying further, we get:
log(96)
Combining the Two Parts
Now, we can combine the two simplified expressions:
(-log(10))(log(96))
Simplifying further, we get:
-log(10^(log(96)))
-log(960)
And that's the simplified expression!
Conclusion
In this article, we have successfully simplified the expression (log 21 - log 210)(log 16 + log 1/6) using the properties of logarithms and algebraic manipulations. The final simplified expression is -log(960).
