# Solve $2+5\ln{x}=21$: Find $x$

• MHB
• karush
In summary, the conversation is about solving the equation $2+5\ln{x}=21$ by isolating $\ln{x}$ and then using the definition of logarithms to solve for $x$. The use of fractional exponents is discussed, and the conversation ends with a mention of using OrangeDox to track the popularity of shared files.
karush
Gold Member
MHB
$\tiny{6.1.07 kilana HS}$
Solve $2+5\ln{x}=21$
\$\begin{array}{rlll} \textsf{isolate} &\ln{x} &=\dfrac{19}{5} &(1)\\ \textsf{then} & &= &(2)\\ \textsf{then} & &= &(3)\\ \textsf{hence} & &= &(4) \end{array}$
ok for (2) I presume e thru then calculate for x
just strange to see a fraction as an e exponent
tryin array on these no sure if its better :unsure:

$$\displaystyle ln(x) = a \implies x = e^a$$

Does it make more sense if you think of it that way?

-Dan

You understand that an exponent is just a number, don't you? An exponent can be an integer, or a fraction, an irrational number, or a complex number.

roger

Country Boy said:
You understand that an exponent is just a number, don't you? An exponent can be an integer, or a fraction, an irrational number, or a complex number.
Or even a matrix... Buwahahahaha!

-Dan

https://dl.orangedox.com/QS7cBvdKw55RQUbliE

this is preliminary test to see if this works
but anyway I am trying to make a collection of 25 or more pre calc problems that came form students here on Oahu
I run a counter on the views and downloads, an earlier count it was over 50,000 on the MHB views
so it has been an awsome help. Hopefully more student from the island will join the forum when school starts up again
Im using OrangeDox because it keeps track of what happens with you posted files

## 1. What is the equation $2+5\ln{x}=21$?

The equation $2+5\ln{x}=21$ is a logarithmic equation that involves the natural logarithm function. It is asking to find the value of $x$ that satisfies the equation.

## 2. How do I solve $2+5\ln{x}=21$?

To solve $2+5\ln{x}=21$, you can use basic algebraic techniques to isolate the variable $x$ on one side of the equation. This may involve using the properties of logarithms and exponentials, as well as simplifying the equation by combining like terms.

## 3. What is the domain of the solution to $2+5\ln{x}=21$?

The domain of the solution to $2+5\ln{x}=21$ is all positive real numbers, since logarithms are only defined for positive values.

## 4. Can I use a calculator to solve $2+5\ln{x}=21$?

Yes, you can use a calculator to solve $2+5\ln{x}=21$. However, you may need to use the "ln" or "log" function on your calculator to find the value of the natural logarithm. Make sure to check your calculator's user manual for instructions on how to use these functions.

## 5. Is there more than one solution to $2+5\ln{x}=21$?

Yes, there can be more than one solution to $2+5\ln{x}=21$. Since the natural logarithm is a one-to-one function, there can only be one value of $x$ that satisfies the equation. However, this value may be expressed in different forms, such as an exact value or a decimal approximation.

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