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Submitted : 2018-06-14 07:26:58    Popularity:     

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solve for x
-3e^9x-1+6=-58

Answers:

-3e^9x - 1 + 6 = -58
-3e^(9x) = -63
e^(9x) = 21
Real solution:
x ≈ 0.33828

- 3.e^(9x - 1) + 6 = - 58

- 3.e^(9x - 1) = - 58 - 6

- 3.e^(9x - 1) = - 64

e^(9x - 1) = 64/3

Ln[e^(9x - 1)] = Ln(64/3) → you know that: Ln(x^a)= a.Ln(x)

(9x - 1).Ln(e) = Ln(64/3) → recall: Ln(e) = 1

9x - 1 = Ln(64/3)

9x = Ln(64/3) + 1

x = [Ln(64/3) + 1]/9 → to go further

x = [Ln(64) - Ln(3) + 1]/9 → you know that: Ln(64) = Ln(2^6) = 6.Ln(2)

x = [6.Ln(2) - Ln(3) + 1]/9

x ≈ 0.4511412

(-3e^9)x - 1 + 6 = -58
(-3e^9)x = -58 + 1 - 6
(-3e^9)x = -63
x = (-63) / (-3e^9)
x = 21 / (e^9)
x =~ 0.0025916058858202705394503705053307

Or did you mean:
-3e^(9x - 1) + 6 = -58
-3e^(9x - 1) = -58 - 6
-3e^(9x - 1) = -64
e^(9x - 1) = (-64) / (-3)
e^(9x - 1) = 64/3
9x - 1 = ln(64/3) + 2*i*pi*n, for any integer n
9x = ln(64/3) + 1 + 2*i*pi*n, for any integer n
x = (ln(64/3) + 1 + 2*i*pi*n) / 9, for any integer n
x =~ 0.45114119941017357390090527686961 + 0.69813170079773183076947630739545*i*n, for any integer n
If x is a real number, then n = 0, so x = (ln(64/3) + 1) / 9 =~ 0.45114119941017357390090527686961

-3 * e^(9x - 1) + 6 = -58.

-3 * e^(9x - 1) = -58 - 6.

-3 * e^(9x - 1) = -64.

e^(9x - 1) = -64/(-3).

e^(9x - 1) = 64/3.

9x - 1 = ln(64/3).

9x = ln(64/3) + 1.


===> x = [ln(64/3) + 1]/9 (≃ 0.451 to 3 d.p.).

-3e^9x-1+6=-58
this is very ambiguous, I could interpret it dozens of ways.

guess 1:
–3e^(9x) – 1 + 6 = –58
–3e^(9x) = –58 + 1 – 6 = –63
e^(9x) = 21
ln(e^(9x)) = ln 21
9x = 3.0445
x = 0.3383

option 2
–3(e^9)x – 1 + 6 = –58
–3(e^9)x = –63
x = 21/e^9 = 0.002592

etc



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