Is 1=e^x a transcendental equation ?

Question

also can you give me other examples of transcendental equations ?

even though many transcendentals can't be solved via algebra can't some transcendental equations actually be solved by algebra (like 1= e^x if transcendental)

thanks in advance

Answer 1

When x is in an exponent within an equation, you have a transcendental function.

x = sin(x)

x² = 5ⁿ

1/x = log(x)

3ⁿ = 7·n

sin(x) = ln(x)

Many ones can be solved, but many ones do not have an algebraic solution. This is especially the case when completely different types of transcendental functions are used together or when one is used with algebraic functions.