# When are you supposed to take the natural log of both sides of an equation?

• Jurrasic
Also, b is a positive number, so multiplying both sides of bx=y by b gives bbx=by, or bx=by. This is why taking the log of both sides can be useful.In summary, taking the natural log of both sides of an equation can be helpful when dealing with exponential functions and can be used to reveal a formula for an unknown variable. The key is to use inverse operations to simplify the equation and solve for the variable.
Jurrasic
It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?

Last edited:
You use "e" to cancel out a natural log of an equation.

Jurrasic said:
It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?

If you have an equation that involves exponents, that's a natural for taking the log of both sides.

For example, if ex + 2 = 3, we can take the natural log of both sides to get
ln(ex + 2) = ln(3)
x + 2 = ln(3)
x = -2 + ln(3) ≈ -1.307

Jurrasic said:
It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?

The key to understand is you use an inverse operation or a sequence of inverse operations to reveal a formula for an unknown but sought variable. An exponential function is the inverse of a logarithmic function. You would do something similar if you wanted to clear for an additive inverse or a multiplicative inverse.

Mark44's example to illustrate is a good one.

Note that logb(bx)=x

## What is the purpose of taking the natural log of both sides of an equation?

Taking the natural log of both sides of an equation is a common technique used in mathematics and science to simplify an equation so that it can be solved more easily. It also allows for easier manipulation of the equation and can help in identifying patterns or relationships between variables.

## When is it necessary to take the natural log of both sides of an equation?

Taking the natural log of both sides of an equation is usually necessary when the equation contains exponential or logarithmic functions. It is also commonly used when solving equations involving growth or decay rates, as well as in calculus and statistics.

## What are the steps for taking the natural log of both sides of an equation?

The steps for taking the natural log of both sides of an equation are as follows:

1. Identify the exponential or logarithmic function in the equation.
2. Apply the natural log function to both sides of the equation.
3. Use the properties of logarithms to simplify the equation.
4. Solve for the variable of interest.

## Can you take the natural log of any type of equation?

No, the natural log can only be taken of equations that involve exponential or logarithmic functions. It cannot be applied to equations with other types of functions, such as trigonometric or polynomial functions.

## How does taking the natural log of both sides of an equation affect the solution?

Taking the natural log of both sides of an equation can change the form of the equation, making it easier to solve. It can also help in identifying patterns or relationships between variables. However, it is important to remember to undo the natural log by taking the exponential of both sides in order to find the final solution.

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