Question

Să se determine soluțiile reale ale ecuației 2 la puterea x-1 + 2 la puterea x =12

Answer 1

 

$\displaystyle\\2^{x-1}+2^x=12\\\\2^{x-1}+2^{x-1+1}=12\\\\2^{x-1}+2^{x-1}\cdot2^1=12\\\\2^{x-1}\Big(1+2\Big)=12\\\\2^{x-1}\cdot3=12\\\\2^{x-1}=\frac{12}{3}\\\\2^{x-1}=4\\\\2^{x-1}=2^2\\\\ x-1=2\\\\x=2+1\\\\\boxed{\bf~x=3}$

 

 

Answer 2

Răspuns:

2 la puterea (x-1) + 2 la puterea x =12

PARANTEZELE!!!!!!!!!!!!!!!!!ORDINEA OPERATIILOR!!!!!!!!!!!!!!!!!!

x=3

Explicație pas cu pas:

2^(x-1)+2^x=12

2^x=t

t/2+t=12

3t/2=12

t=8

2^x=8

2^x=2³

2=2⇒x=3