Solving equations - When to take logarithms?

Thread starter dcgirl16
Start date Jun 14, 2007
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Logarithms Solving equations

In summary, taking logarithms is a useful technique for solving equations with variables in the exponent position. It simplifies equations and converts them into linear ones, making them easier to solve. You should take logarithms when other methods are not working, especially for exponential growth or decay equations. The base of the logarithm should match the base of the exponential term in the equation. You can use logarithms on both sides of an equation as long as the bases match, and there are restrictions to keep in mind such as the input must be positive and the base cannot be 0 or 1. It is important to check for these restrictions when solving equations with logarithms.

Jun 14, 2007

dcgirl16

How do i know when to take the ln of both sides to solve an equation for example would i for y=10^(1-x)-(1-x)^10

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Jun 15, 2007

olgranpappy

Homework Helper

you try it and see if it works

Jun 15, 2007

Gib Z

Homework Helper

If theirs an 'e' on either side and you want to get rid of it, ie you have e^x and you only want x.

1. What is the purpose of taking logarithms when solving equations?

Taking logarithms is a helpful technique when solving equations because it allows us to simplify and solve for variables that are in the exponent position. It also helps to convert exponential equations into linear ones, making them easier to solve.

2. When should I take logarithms when solving equations?

You should take logarithms when solving equations when you have variables in the exponent position, and you are having difficulty solving for them using other methods. This is especially useful when solving for variables in exponential growth or decay equations.

3. How do I know which base to use when taking logarithms?

The base of the logarithm should match the base of the exponential term in the equation. For example, if the equation has a base of 2, then you should use a base 2 logarithm. If you are solving for a variable in an exponential growth or decay equation, you can use any base for the logarithm, as long as it is consistent on both sides of the equation.

4. Can I take logarithms on both sides of an equation?

Yes, you can take logarithms on both sides of an equation as long as the bases match. This is known as the logarithmic property of equality, and it allows us to simplify and solve equations with logarithms.

5. Are there any restrictions when taking logarithms?

Yes, there are a few restrictions when taking logarithms. The argument (input) of the logarithm must be positive, and the base of the logarithm must be greater than 0 and not equal to 1. Additionally, the logarithm of 0 is undefined, so the input cannot be 0. It is important to check for these restrictions when solving equations with logarithms.