Question

Determine all real values of x given that 6^(x+1)-6^x=3^(x+4)-3^x

Answer 1

apparently the answer is 4, but i am not sure exactly how. somehow this can be rewritten. let me try with paper

Answer 2

\[6^x(6-1)=3^x(3^4-3)\] maybe that is a good start

Answer 3

then
\[5\times 6^x=80\times 3^x\]

Answer 4

\[6^x=16\times 3^x\]
\[\frac{6^x}{3^x}=16\]
\[2^x=16\]
\[x=4\] there i knew it was possible

Answer 5

thanks!