Question

Să se afle x din următoarele relaţii:
a) 3 la 2x + 9 la x ∙3 + 3 la (2x+3 )= 2511
b) 2 la (x+3) + 2 la (x+2) + 2 (x+1) + 2 la x = 240.

Answer 1

[tex]3^{2x}+3\cdot9^x+3^{2x+3}=2511\\ 3^{2x}+3\cdot3^{2x}++3^3\cdot3^{2x}=2511\\ 3^{2x}(1+3+3^3)=2511\\ 31\cdot3^{2x}=2511\\ 3^{2x}=\frac{2511}{31}=81=3^4\\ 2x=4\Rightarrow \boxed{x=2}\\ \\ 2^{x+3}+2^{x+2}+2^{x+1}+2^x=240\\ 2^3\cdot2^x+2^2\cdot2^x+2\cdot2^x+2^x=240\\ 2^x(8+4+2+1)=240\\ 2^x\cdot15=240\\ 2^x=\frac{240}{15}=16=2^4\\ \Rightarrow\boxed{x=4}[/tex]