Question

Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.

In x - In(x - 6) = 3

Answer 1

`x=(6e^3)/(e^3-1)`

Explanation:

`ln x - ln(x - 6) = 3`

Apply natural log property

ln mn=ln m + ln(n), ln(m/n)=ln(m)-ln(n)

`ln x - ln(x - 6) = 3`

`ln((x)/(x-6) )=3`

All natural log has base 'e'

`(x)/(x-6) =e^3`

cross multiply

`x=e^3(x-6)`

`x=e^3x-6e^3`

add 6e^3 on both sides and -x on both sides

`6e^3=e^3x-x`

`6e^3=x(e^3-1)`

Divide e^3-1 on both sides

`x=(6e^3)/(e^3-1)`