The natural base e raised to the power of lna is equal to the argument of the natural logarithm, a.
See solution.
Practice makes perfect
First we will describe the error made, then we will solve the equation in a correct way.
Describing the Error
Let's analyze the given solution step by step, and look for the error that was made.
ln4x=5 ⇔ e^(ln4x)=e^5
The first step is correct. The natural base e was raised to the power of both sides of the first equation. Let's take a look at the next step.
e^(ln4x)=e^5 ⇔ 4x=5
This is the step in which the error was made. The left-hand side of the equation was simplified correctly — e raised to the power of lna is equal to the argument of the natural logarithm, a. However, there are no properties that would allow us to simplify the right-hand side of the equation as it was done.
Correcting the Error
Now we will solve the given equation.
ln4x=5
Our first step will be the same as the first step in the given solution.
ln4x=5 ⇔ e^(ln4x)=e^5
Next, we will simplify the left-hand side of the equation. Recall that e raised to the power of lna is equal to the argument of the natural logarithm, a.
e^(ln4x)=e^5 ⇔ 4x=e^5
Finally, let's isolate x on the left-hand side of the equation.
