Question

Solve the exponential equation. Exact answers only 3e^(x-1)=2+e^(x-1)

Answer 1

subtracting \(e^{x-1}\) from either side gives us what?

Answer 2

wait 3+2

Answer 3

or 3=2

Answer 4

@oldrin.bataku

Answer 5

:/ netta pretend the \(e^{x-1}\) is another variable like \(z\):$$3z=2+z$$how would you solve for \(z\) above?

Answer 6

sub both sides by z

Answer 7

@oldrin.bataku

Answer 8

and you get \(2z=2\), yes? so \(z=1\))? well here we have \(z=e^{x-1}\) hence:$$e^{x-2}=1$$can you tell me what exponent makes a power yield \(1\)?

Answer 9

is it 1

Answer 10

@netta nah, \(0\):$$2^0=1\\3^0=1\\\dots$$ so we know the exponent of \(e^{x-1}\) (I made a typo above) needs to be \(0\):$$x-1=0\\x=1$$