Help solving log (natural number) equation

Thread starter Muskox
Start date Mar 17, 2006
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Log

In summary, a natural number is a positive integer that is not a fraction or decimal. A logarithm is the inverse operation of exponentiation and is used to solve exponential equations. To solve a logarithmic equation, you can use the properties of logarithms or rewrite it in exponential form. The natural log function, ln, is the logarithm with base e and is commonly used in math and science. Yes, you can use a calculator to solve a logarithmic equation, either through the ln button or by graphing the equation on a graphing calculator.

Mar 17, 2006

Muskox

I am stuck on finding the solution to this problem.

2lnX = 2 + ln(X-1)

Please show all steps for the solution.

Thank you.

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Mar 17, 2006

chroot

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Science Advisor

Gold Member

Try raising both sides by e. Use algebra to simplify.

- Warren

Mar 17, 2006

Muskox

I get this far.
X^2/X-1 = e^2
X^2 = e^2(X-1)
x^2 = e^2 X - e^2

Mar 17, 2006

Integral

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Science Advisor

Gold Member

You now have a quadraic equation in x. Remember e² is just a number.

What is a natural number?

A natural number is a positive integer (1, 2, 3, etc.) that is not a fraction or decimal.

What is a logarithm?

A logarithm is the inverse operation of exponentiation. It is used to solve exponential equations, and represents the power to which a base number must be raised to equal a given number.

How do I solve a logarithmic equation?

To solve a logarithmic equation, you can use the properties of logarithms, such as the product, quotient, and power rules. You can also use the fact that logarithms and exponentials are inverse operations to rewrite the equation in exponential form.

What is the natural log (ln) function?

The natural log function, denoted as ln, is the logarithm with base e (the natural logarithmic base, approximately equal to 2.71828). It is commonly used in mathematics and science to model exponential growth and decay.

Can I use a calculator to solve a logarithmic equation?

Yes, most scientific calculators have a button for the natural log (ln) function. You can also use a graphing calculator to graph the logarithmic equation and find the solution(s) by finding the intersection point(s) with the x-axis.