Question

If <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${36}^x$ = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${216}^4$, then what is the value of x?

• A. 7
• B. 6
• C. 10
• D. 5

Answer 1

The correct option is B 6

Since 36 = $6^2$, ${36}^x$ = $(6^2{)}^x$ = $6^{2x}$
Also, since 36 $\times$ 6 = 216, 216 = $6^3$
Thus, ${216}^4$ = $(6^3{)}^4$ = $6^{3\times 4}$ = $6^{12}$
So the original equation, ${36}^x$ = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${216}^4$ becomes
$6^{2x}$ = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $6^{12}$
Equating the exponents as the bases are the same, we get,
$2x$ = 12
=> $x$ = 12 $÷$ 2 = 6