how to solve this logarithm question

Question

0=15000(1.003)^n - 71052.63((1.003^n)-1)

Answer 1

15000(1.003)ⁿ = 71052.63[(1.003)ⁿ]^-1      

 

15000(1.003)ⁿ = 71052.63/(1.003)ⁿ      because n*(-1) = -n so it becomes +n if you divide, as shown

 

(1.003)ⁿ (1.003)ⁿ = 71052.63/15000 = 4.736842

 

(1.003)²ⁿ = 4.736842

 

2n log1.003 = log 4.736842

 

           n     =  log 4.736842/(2*log1.003)

           n     = 259.617 ANSWER