Can one use logarithms to solve the equations 2=3^x+x and 2=3^x x? Could someone explain how would you solve: 2=3^x+x and 2=3^x⋅x I can only solve halfway through. And why is 10^(log(x))=x Thanks
Can one use logarithms to solve the equations and ?
I can only solve halfway through.
And why is
Answer & Explanation
By definition, a log is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Below is a simple example,
Also, the solutions to both of those problems cannot be found using elementary functions.
To solve these equations, we must use the Lambert W function. This function will provide the value of in equations that take the form
Since you're curious, here are the solutions
And after some trial and error,