solve for x:
a)e^x=5
b) lnx=2
Take the ln of each side;
x=ln5
take the antiln of each side.
x=e^2
These equations can be solved if we understand the relationship between ex and log(x).
if ex = y, then log(y)=x
and vice versa.
Example:
ex=3, then x=ln(3)=1.0986
If ln(x)=4, then x=e4=54.598
If you want to post your answers for checking, feel free to do so.
a) To solve the equation e^x = 5, you can use the natural logarithm function. The natural logarithm function, denoted as ln(x), is the inverse of the exponential function e^x. By taking the natural logarithm of both sides of the equation, we can isolate the variable x.
Using the natural logarithm:
ln(e^x) = ln(5)
x = ln(5)
Therefore, the solution for x is x = ln(5).
b) To solve the equation ln(x) = 2, you can use the exponential function. The exponential function e^x is the inverse of the natural logarithm function ln(x). By taking the exponential function of both sides of the equation, we can isolate the variable x.
Using the exponential function:
e^(ln(x)) = e^2
x = e^2
Therefore, the solution for x is x = e^2.