Question

Find roots :- 4^x - 8( 2^x ) + 7 = 0 .​

Answer 1

Answer:

→ roots are 0 and $log_{2}(7)$ .

Step-by-step explanation:

Let $2^x$ = t.

→ $2^{2x}$ - 8($2^x$) + 7 = 0 .

→ t² - 8t + 7 = 0 .

→ t² - 7t - t + 7 = 0 .

→ t( t - 7 ) - 1( t - 7 ) = 0 .

→ ( t - 1 ) ( t - 7 ) = 0 .

→ t = 1 or 7 .

→ $2^x$ = 1 or 7 .

→ $2^x$ = $2^0$ or $2^x$ = 7 .

→ x = 0 or $2^x$ = 7 .

$\therefore$ x = 0 or x = $log_{2}(7)$ .

Hence, roots are 0 and $log_{2}(7)$ .