# Find the solution of this ln equation

• transgalactic
In summary, an ln equation is an equation that contains the natural logarithm function, written as ln(x). To solve an ln equation, the ln term must be isolated and logarithm properties must be used to simplify the equation. Multiple solutions are possible for ln equations, and it is important to check all potential solutions. Negative solutions for ln equations are not allowed, and special cases such as absolute value and equal to 0 or 1 must be considered when solving ln equations.
transgalactic
find the solution of this ln equation:
ax=lnx

i tried:
$$e^{(ax)}=x$$
$$e^{(ax)}-x=0$$

what to do next??
i thought of building a taylor series around 0 for ln
but ln(0) is undefined

??

Last edited:
I'm not entirely sure, but I think such equations must be solved with a numerical method, such as Newton-Rhapson.

When there is any solution there are two I think.

## 1. What is an ln equation?

An ln equation is an equation that contains the natural logarithm function, written as ln(x). This function represents the inverse of the exponential function, and is commonly used in mathematics and science to solve for the value of x.

## 2. How do I solve an ln equation?

To solve an ln equation, you must isolate the ln term on one side of the equation and use the properties of logarithms to simplify the equation. Then, you can exponentiate both sides to solve for the value of x. It is important to check your solution by plugging it back into the original equation.

## 3. Can an ln equation have multiple solutions?

Yes, an ln equation can have multiple solutions. This occurs when the original equation contains multiple logarithmic terms, or when the logarithmic term is raised to a power. It is important to check all potential solutions when solving an ln equation.

## 4. What if the ln equation has a negative solution?

If an ln equation has a negative solution, it means that the equation is undefined for that value of x. This can occur when the argument of the ln function is negative, which is not allowed. In this case, the solution set is restricted to positive values of x.

## 5. Are there any special cases when solving ln equations?

Yes, there are a few special cases when solving ln equations. One is when the ln equation contains an absolute value, in which case you must consider both the positive and negative solutions. Another is when the ln equation is equal to 1, in which case the solution set is x = 0. Lastly, if the ln equation is equal to 0, there is no solution because ln(0) is undefined.

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