Solve the exponential equation. Express the solution in terms of natural logarithms. Then, use a calculator to obtain a decimal approximation for the solution.
e^x = 20.9
What is the solution in terms of natural logarithms?
The solution set is { }.
Take ln of both sides.
ln of e^x is x
x = ln 20.9
Use a calculator to find x by taking the ln of 20.9
simply convert e^x = 20.9
to the corresponding logarithmic equation.
You MUST know how to do this.
then simply use your calculator
To solve the exponential equation e^x = 20.9 in terms of natural logarithms, we can take the natural logarithm (ln) of both sides of the equation. This will allow us to isolate x.
ln(e^x) = ln(20.9)
Since ln and e are inverse functions, ln(e^x) and x will cancel out on the left side of the equation, leaving us with:
x = ln(20.9)
Therefore, the solution in terms of natural logarithms for the given equation is x = ln(20.9).
Now, let's use a calculator to obtain a decimal approximation for the solution:
Using a calculator, ln(20.9) is approximately 3.035. Hence, the decimal approximation for the solution is x ≈ 3.035.
To solve the exponential equation e^x = 20.9 in terms of natural logarithms, we can take the natural logarithm (ln) of both sides of the equation.
ln(e^x) = ln(20.9)
Using the property of logarithms that ln(e^a) = a, we can simplify the equation to:
x = ln(20.9)
So the solution to the exponential equation e^x = 20.9 in terms of natural logarithms is x = ln(20.9).
To obtain a decimal approximation for this solution, you can use a calculator.