Question

How do you solve 216^x-1=6

Answer 1

$216^{x-1}=6 \\ (6^3)^{x-1}=6 \\ 6^{3(x-1)}=6 \\ 6^{3x-3}=6^1 \\ 3x-3=1 \\ 3x=4 \\ x=\frac{4}{3}$

Answer 2

$216^{x-1}=6\\ ln(216^{x-1})=ln(6)\\ (x-1)ln(216)=ln(6)\\ xln(216)-ln(216)=ln(6)\\ xln(216)=ln(6)+ln(216)\\ x= \frac{ln(6)+ln(216)}{ln(216)} \approx 1,333$