Verified answer

2^(3x + 2) - 2^(3x + 1) + 2^(3x - 1) = 50^(x)

[2^(3x) * 2^(2)] - [2^(3x) * 2^(1)] + [2^(3x) * 2^(-1)] = 50^(x)

4[2^(3x)] - 2[2^(3x)] + (1/2)[2^(3x)] = 50^(x)

[2^(3x)] * [4 - 2 + (1/2)] = 50^(x)

[2^(3x)] * (5/2) = 50^(x)

Ln { [2^(3x)] * (5/2) } = Ln[50^(x)]

Ln[2^(3x)] + Ln(5/2) = x.Ln(50)

3x.Ln(2) + Ln(5/2) = x.Ln(50)

3x.Ln(2) - x.Ln(50) = - Ln(5/2)

x.[3Ln(2) - Ln(50)] = - Ln(5/2)

x.[3Ln(2) - Ln(2 * 5²)] = - Ln(5/2)

x.[3Ln(2) - Ln(2) - Ln(5²)] = - Ln(5/2)

x.[2Ln(2) - 2Ln(5)] = - Ln(5/2)

2x.[Ln(2) - Ln(5)] = - Ln(5/2)

2x.[Ln(2/5)] = - Ln(5/2)

2x = - Ln(5/2) / Ln(2/5)

2x = - Ln(5/2) / - Ln(5/2)

2x = 1

x = 1/2

Salut,

On factorise 2^3x dans le prermier membre :

2,5.2^3x = 50^x → ln(5/2) + 3.ln(2).x = ln(50).x

→ x = [ln(3/2)]/[2.ln(5) + ln(2) - 3.ln(2)] = ½ ln(5/2)/ln(5/2)

→ x = ½

@+ ;)

< sauf erreur(s) >

X=0.5

Utiliser le calculateur wolfram's math

(lien ci -dessous)