Question

3.3^+4.3^x+ 3^x = 648 find x

Answer 1

Solution is in the attachment

Answer 2

Solution :

$\mathtt{3.3 {}^{x} + 4.3 {}^{x} + 3 {}^{x} = 648} \\ \\ \mathtt{3 \times 3 {}^{x} + 4 \times 3 {}^{x} + 3 {}^{x} = 648} \\ \\ \mathtt{3 {}^{x}(3 + 4 + 1) = 648 } \\ \\ \mathtt{3 {}^{x} \times 8 = 648 } \\ \\ \mathtt{ 3{}^{x} = \frac{648}{8} } \\ \\ \mathtt{3 {}^{x} = 81 } \\ \\ \mathtt{ \cancel3 { \: }^{x} = \cancel3 \: {}^{4} } \\ \\ \mathtt{ \bold{ \therefore x = 4}}$
Verification :

Putting the value of x, we get ;

$\mathtt{3.3 {}^{x} + 4.3 {}^{x} + 3 {}^{x} = 648} \\ \\ \mathtt{3 \times 3 {}^{4} + 4 \times 3 {}^{4} + 3 {}^{4} = 648} \\ \\ \mathtt{243 + 324 + 81 = 648} \\ \\ \mathtt{628 = 628} \\ \\ \bold{ \therefore LHS = RHS}$

Hence, the value of x = 4.