30000 = (15*(1-1.5^n))/(1-1.5) what is n? : - )

Rearrange as (1-1.5)*30000/15 = 1 - 1.5ⁿ

 

Then  1.5ⁿ = 1 - (1-1.5)*30000/15

 

Take logs of both sides and use log(a^b) = b*log(a)

 

n*log(1.5) = log(1 - (1-1.5)*30000/15)

 

Divide both sides by log(1.5)

 

$${\mathtt{n}} = {\frac{{log}_{10}\left({\mathtt{1}}{\mathtt{\,-\,}}{\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{1.5}}\right){\mathtt{\,\times\,}}{\mathtt{30\,000}}}{{\mathtt{15}}}}\right)}{{log}_{10}\left({\mathtt{1.5}}\right)}} \Rightarrow {\mathtt{n}} = {\mathtt{17.039\: \!085\: \!832\: \!934\: \!851}}$$

 

n ≈ 17

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