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
