What is the Basic Concept of Logarithms in Calculus?

Thread starter thomasrules
Start date Feb 3, 2005
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Calculus Logarithms

In summary, a logarithm is the inverse function of an exponential function and is used to solve for the exponent in an exponential equation. It has properties such as the product, quotient, and power properties. To solve logarithmic equations, the logarithm must be isolated and the properties of logarithms can be used. Logarithms also play a role in calculus, specifically in solving problems involving exponential growth and decay as well as in integration and differentiation. Finally, logarithmic functions can be graphed, with the shape of the curve depending on the base of the logarithm.

Feb 3, 2005

thomasrules

I tried this question and can't get it:

log subscript 3(9 times (9)^(1/5))

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Feb 3, 2005

MathStudent

realize that
[tex] 9 \ * \ 9^\frac{1}{5} = 9^{1 + \frac{1}{5}} = 9^\frac{6}{5}[/tex]

Then use properties of logs

Feb 3, 2005

thomasrules

thank you stranger

Related to What is the Basic Concept of Logarithms in Calculus?

1. What is a logarithm?

A logarithm is the inverse function of an exponential function. It is used to solve for the exponent in an exponential equation, and is represented as log_b(x), where b is the base and x is the value being raised to that power.

2. What are the properties of logarithms?

Some common properties of logarithms include the product property, quotient property, and power property. The product property states that log_b(xy) = log_b(x) + log_b(y). The quotient property states that log_b(x/y) = log_b(x) - log_b(y). The power property states that log_b(xⁿ) = n * log_b(x).

3. How do you solve logarithmic equations?

To solve a logarithmic equation, you must first isolate the logarithm on one side of the equation. Then, use the properties of logarithms to simplify the equation. Finally, use the inverse operation of logarithms, exponentiation, to solve for the variable.

4. How do logarithms relate to calculus?

Logarithms are used in calculus to solve problems involving exponential growth and decay. They are also used in integration and differentiation, as logarithmic functions have unique derivatives and integrals.

5. Can logarithmic functions be graphed?

Yes, logarithmic functions can be graphed. The graph of a logarithmic function is a curve that approaches but never touches the x-axis. The shape of the curve depends on the base of the logarithm, with larger bases resulting in steeper curves.