What are the 7 laws of logarithms?

Question

CramX · Accepted Answer

Step 1: : The first law of logarithms, also known as the product rule, states that the logarithm of a product is equal to the sum of the logarithms of the factors.. Step 2: : The second law, or quotient rule, states that the logarithm of a quotient is equal to the difference between the logarithms of the dividend and the divisor.. Step 3: : The third law, or power rule, states that the logarithm of a number raised to an exponent is equal to the product of the exponent and the logarithm of the number.. Step 4: : The fourth law, or change of base formula, states that any logarithm can be converted to a different base using the following formula:. Step 5: : The fifth law states that the logarithm of 1 is always 0 for any base.. Step 6: : The sixth law states that the logarithm of the base is always 1.. Step 7: : The seventh law states that if the logarithm of a number is 0, then the number must be equal to 1.. Final Answer: The seven laws of logarithms are: 1. Product rule: $\log\_b(xy) = \log\_b(x) + \log\_b(y)$ 2. Quotient rule: $\log\_b\left(\frac{x}{y}\right) = \log\_b(x) - \log\_b(y)$ 3. Power rule: $\log\_b(x^y) = y\log\_b(x)$ 4. Change of base formula: $\log\_a(x) = \frac{\log\_b(x)}{\log\_b(a)}$ 5. Logarithm of 1: $\log\_b(1) = 0$ 6. Logarithm of the base: $\log\_b(b) = 1$ 7. If the logarithm of a number is 0, the number is 1: $\log\_b(x) = 0 \Rightarrow x = 1

Q
QuestionMathematics

Answer

Full Solution Locked

Step 1:
: The first law of logarithms, also known as the product rule, states that the logarithm of a product is equal to the sum of the logarithms of the factors.

Step 2:
: The second law, or quotient rule, states that the logarithm of a quotient is equal to the difference between the logarithms of the dividend and the divisor.

Step 3:
: The third law, or power rule, states that the logarithm of a number raised to an exponent is equal to the product of the exponent and the logarithm of the number.

Final Answer

Need Help with Homework?

Related Questions

Company

Explore

Study Tools

QQuestionMathematics

AnswerHelpful