Question
Asked Aug 1, 2019
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Solve for x: e^ x^ 2+6 = e^5x

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Expert Answer

Step 1

Given expression is

e*2+6e5x
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e*2+6e5x

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Step 2

Taking log with the bas...

log.e+6log.e5x
(x26)log.e 5xlog e
(Since, logaa 1)
(x? + 6) х 1 — 5х х1
— х? +6 %3 5х
— х2 — 5х + 6 — 0
— х2 — 2х — Зх + 6 — 0
x(х — 2) — 3(х — 2) 3 0
— (х — 2) (х — 3) - 0
Either x
0 or x 3 0
2
х%3D 2
= 3
or x
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log.e+6log.e5x (x26)log.e 5xlog e (Since, logaa 1) (x? + 6) х 1 — 5х х1 — х? +6 %3 5х — х2 — 5х + 6 — 0 — х2 — 2х — Зх + 6 — 0 x(х — 2) — 3(х — 2) 3 0 — (х — 2) (х — 3) - 0 Either x 0 or x 3 0 2 х%3D 2 = 3 or x

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