You can put this solution on YOUR website! ln(2x) = 6
With the logarithm isolated, like this, the next step is to rewrite the equation in exponential form. In general is equivalent to . Using this pattern and the fact that the base of ln is "e" we get:
Now we just divide by 2:
Before we're finished we must chack our answer. This is required for equations like this one. You must ensure that your solution makes the argument of the logarithm positive. If it happens to make the argument zero or negative then you must reject it (even if it is the only "solution" you found). These rejected "solutions" can happen even if no mistakes have been made.
Use the original equation to check:
ln(2x) = 6
Checking :
ln(2(e^6/2)) = 6
which simplifies to
ln(e^6) = 6
Since e to any power is positive there is no reason to reject the solution. (This is the required part of the check. The rest is optional. You are welcome to finish it to see if we made any mistakes.)
So is the solution. This is an exact expression for the solution to your equation. If you need a decimal approximation, then replace "e" with 2.7182818284590451 (or some rounded off version of it) and use your calculator to raise it to the sixth power and then divide by 2.
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