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# What is the solution of the equation 5e^(x-3)=4 ?

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- MichaelLv 72 months agoFavorite Answer
5e^(x - 3) = 4

Divide both sides by 5

e^(x - 3) = .8

Take the ln of both sides

x - 3 = ln .8

add 3 to both sides

x = ln .8 + 3

x ≈ 2.77685644868579 <––––––

- PhilipLv 62 months ago
5e^(x-3) = 4, ie., e^(x-3) = (4/5) = 0.8. Take ln of both sides to get x-3 = ln(0.8).

Then x = 3+ ln(0.8) = 3-0.2231435513 = 2.776856449.

- llafferLv 72 months ago
5e^(x - 3) = 4

I would start by dividing both sides by 5:

e^(x - 3) = 4/5

Natural log of both sides:

x - 3 = ln(4/5)

Add 3 to both sides:

x = 3 + ln(4/5)

or:

x = 3 + ln(4) - ln(5)

- ?Lv 72 months ago
5 eˣ⁻³ = 4

ln 5 + (x-3) ln e = ln 4

ln 5 + (x-3) (1) = ln 4

x - 3 = ln 4 - ln 5

x = ln 4 - ln 5 + 3

x = 2.77686................ANS (rounded)

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- 2 months ago
take logs of both sides......ln5+(x-3)ln(e)=ln 4, but ln(e)=1, so x-3 = ln 4 - lin 5, so x= 3+ln(4/5)

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