Question

Log 2 16+ log 1/3 9​

Answer 1

Объяснение:

$log_{2}(16) + log_{ \frac{1}{3} }(9 )$

= 4 + (-2) = 2

Answer 2

Logarithm Basics

To answer your question, let's start with some basics about logarithms. In mathematics, logarithms are used to solve exponential equations and to express a given number as an exponent. The logarithm of a number is essentially the exponent to which another fixed number, called the base, must be raised to produce that number.

The most commonly used logarithm is the natural logarithm, which has a base of e, a mathematical constant approximately equal to 2.71828. However, in your question, you provided logarithms with different bases.

Logarithm Properties

In general, logarithms have several properties that can help simplify calculations and solve equations. Two important properties are:

1. Product Rule: log(a * b) = log(a) + log(b) 2. Quotient Rule: log(a / b) = log(a) - log(b)

These properties allow us to break down logarithms of products or quotients into sums or differences of logarithms.

Solving Logarithmic Equations

Now, let's solve the equation you provided: log(2, 16) + log(1/3, 9).

First, let's simplify each logarithm individually:

1. log(2, 16): This logarithm has a base of 2 and a value of 16. We need to find the exponent to which 2 must be raised to obtain 16. In this case, 2^4 = 16, so log(2, 16) = 4.

2. log(1/3, 9): This logarithm has a base of 1/3 and a value of 9. We need to find the exponent to which 1/3 must be raised to obtain 9. In this case, (1/3)^(-2) = 9, so log(1/3, 9) = -2.

Now, let's add these two logarithms together: 4 + (-2) = 2.

Therefore, the simplified form of the equation log(2, 16) + log(1/3, 9) is 2.

Conclusion

In conclusion, the expression log(2, 16) + log(1/3, 9) simplifies to 2. This means that when you add the logarithms together, the result is 2.