garcia11006 garcia11006
  • 01-06-2020
  • Mathematics
contestada

solve 5^(3x-9)-10=-2
Give the exact solution and an approximate solution to three decimal places.
x = (blank) ≈ (blank)

Respuesta :

eudora eudora
  • 06-06-2020

Answer:

x = 3.431

Step-by-step explanation:

Given equation is,

[tex]5^{(3x-9)}-10=-2[/tex]

[tex]5^{3x-9}-10+10=-2+10[/tex]

[tex]5^{3x-9}=8[/tex]

By taking log on both the sides of the equation,

[tex]\text{log}(5^{3x-9})=\text{log}8[/tex]

(3x - 9)log5 = log8

3x - 9 = [tex]\frac{\text{log}8}{\text{log}5}[/tex]

3x - 9 = 1.292

3x = 9 + 1.292

x = [tex]\frac{10.29202}{3}[/tex]

x = 3.4306

x ≈ 3.431

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