[Solved] Equations

Quadratic Equations

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June 15, 2021 10:39 am

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Staff

(@armor)

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Solve the equation $5^{x+1}=3^{x^2-1}.$

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June 15, 2021 10:40 am

Topic starter

Staff

(@armor)

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317 Posts
156 153 0

$\small 5^{x+1}=3^{x^2-1}\Leftrightarrow (x+1)lg5=(x^2-1)lg3\Leftrightarrow (x+1)[lg5-(x-1)lg3]=0,$ thus

$\small x+1=0$ or $\small lg5-(x-1)lg3=0,$ which imply two solutions

$\small x=-1, x=log_{3}15.$

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