Question

300=400-350(3.2)^(-0.1x)

Answer 1

`x=-10\log_(3.2)(2)/(7)`

Explanation:

Given the equation
`300=400-350\cdot (3.2)^(-0.1x)`

First, subtract 400 from both sides of the equation:

`300-400=400-350\cdot (3.2)^(-0.1x)-400\\ \\-100=-350\cdot (3.2)^(-0.1x)`

Multiply the eequation by -1:

`100=350\cdot (3.2)^(-0.1x)`

Divide it by 350:

`(100)/(350)=(3.2)^(-0.1x)\\ \\(2)/(7)=(3.2)^(-0.1x)`

This equation is equivalent to the equation

`\log_(3.2)(2)/(7)=\log_(3.2)(3.2)^(-0.1x)\\ \\\log_(3.2)(2)/(7)=-0.1x`

Multiply it by -10:

`-10\log_(3.2)(2)/(7)=x`

Hence,

`x=-10\log_(3.2)(2)/(7)`