1 + 3 × 3 log 30: Understanding the Mathematical Expression
In mathematics, expressions like 1 + 3 × 3 log 30 can be daunting at first, but breaking them down into smaller parts can make them more manageable. In this article, we'll dive into the world of logarithms and explore how to evaluate this expression.
What is a Logarithm?
A logarithm is the inverse operation of exponentiation. In simpler terms, it's the power to which a base number must be raised to produce a given value. The most common logarithmic function is the natural logarithm, denoted by ln(x), which has a base of e (approximately 2.718).
Breaking Down the Expression
Let's dissect the expression 1 + 3 × 3 log 30:
- 1: This is a simple constant term.
- 3 × 3: This is a multiplication operation, which equals 9.
- log 30: This is a logarithmic function, which we'll evaluate next.
Evaluating the Logarithmic Function
To evaluate log 30, we need to find the power to which the base (in this case, 10) must be raised to produce 30. Using a calculator or logarithmic tables, we find that:
log 30 ≈ 1.477
Putting it All Together
Now that we have evaluated the logarithmic function, we can plug the value back into the original expression:
1 + 3 × 9 × 1.477
First, multiply 3 and 9:
1 + 27 × 1.477
Next, multiply 27 and 1.477:
1 + 39.729
Finally, add 1 to the result:
40.729
And there you have it! The final answer to the expression 1 + 3 × 3 log 30 is approximately 40.729.
