Answer:
[tex]x=-10\log_{3.2}\dfrac{2}{7}[/tex]
Step-by-step explanation:
Given the equation [tex]300=400-350\cdot (3.2)^{-0.1x}[/tex]
First, subtract 400 from both sides of the equation:
[tex]300-400=400-350\cdot (3.2)^{-0.1x}-400\\ \\-100=-350\cdot (3.2)^{-0.1x}[/tex]
Multiply the eequation by -1:
[tex]100=350\cdot (3.2)^{-0.1x}[/tex]
Divide it by 350:
[tex]\dfrac{100}{350}=(3.2)^{-0.1x}\\ \\\dfrac{2}{7}=(3.2)^{-0.1x}[/tex]
This equation is equivalent to the equation
[tex]\log_{3.2}\dfrac{2}{7}=\log_{3.2}(3.2)^{-0.1x}\\ \\\log_{3.2}\dfrac{2}{7}=-0.1x[/tex]
Multiply it by -10:
[tex]-10\log_{3.2}\dfrac{2}{7}=x[/tex]
Hence,
[tex]x=-10\log_{3.2}\dfrac{2}{7}[/tex]
