Question

solve the equation

Answer 1

\[e^2x-1=(e^3)^- x\] the x in the end is supposed to be with the negative signal but couldn't get it to work

Answer 2

its
e^2x-1 = (e^3)^-x

Answer 3

im guessing the 2x - 1 is all part of the exponent otherwise this is not so easy to solve.
anyway for the right hand side we can multiply exponents raised to an exponent
(e^3)^-x = e^-3x
=> e^(2x-1) = e^-3x
we can cancel the e by taking a log with base e (natural log) to both sides
=>2x-1 = -3x
add like terms and isolate x
x = 1/5