solve the exponential equation. express the solution in terms of natural logarithims. Then, use a calculator to obtain a decimal point approximation for the solution.
e^x=12.3
What is the solution in terms of natural logarithims?
The solution set is ?
e^x = 12.3.
Take log of both sides:
x*Lne = Ln12.3
X = Ln12.3 / Lne.
X = 12.3.
To solve the exponential equation e^x = 12.3 in terms of natural logarithms, we can take the natural logarithm (ln) of both sides of the equation. This property allows us to simplify the equation and isolate the variable.
ln(e^x) = ln(12.3)
Since the natural logarithm and the exponential function are inverse functions, they cancel each other out, leaving us with:
x = ln(12.3)
The solution in terms of natural logarithms is x = ln(12.3).
To obtain a decimal point approximation for the solution, we can use a calculator. Taking the natural logarithm of 12.3 using a calculator:
ln(12.3) ≈ 2.509
So, the decimal point approximation for the solution is x ≈ 2.509.