Solve the exponential Equation.

Question

Solve the exponential Equation.

 

2(1.035)^x-2006 = 15

 

(Do not round until final answer. Then round to four decimal places as needed. Use a comma to seperate answers as needed.)

Answer 1

2(1.035)^(x-2006) = 15

 

log( 2(1.035)^(x-2006) ) = log(15)

 

log(2) + (x-2006) log(1.035) = log(15)

 

(x-2006) log(1.035) = log(15) - log(2)

 

x - 2006 = ( log(15) - log(2) ) / ( log(1.035) )

 

x = 2006 + ( log(15) - log(2) ) / ( log(1.035) )

 

x ≈ 2064.57033305908317 ≈ 2064.5703