Show all the steps to solve the equation

Question

Show all the steps to solve the equation by factoring and not using a "u" substitution method. e-10e* + 21 = 0

Answer 1

e^2x-10e^x+21=0

Assuming that e^x= U

So that e^2x-10e^x+21=0 ---------------------> U²-10U+21=0

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U²-10U+21=0 ?

(U-3) * (U-7)=0

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YOU CAN DO ABOVE THING ON YOUR SCRATCH PAPER AND WRITE THE BELOW PART ONLY ON YOUR WORKSHEET:

e^2x-10e^x+21=0

(e^x-3) * (e^x- 7) = 0 ------------------- BY FACTORING

e^x-3 = 0, e^x=3, x = ln3

e^x-7 = 0, e^x=7, x = ln7

Answer 2

You did it again!!!

ok now as written the equation simplifies to -9e + 20 = 0 ---> e = -21/-9 = 7/3

But because you said FACTORING,

you probably meant e^2 - 10e + 21 = 0

( e - 7 )(e - 3 ) = 0

So e-7 = 0 --> e =7 OR e-3=0 ---> e = 3