Question

9^18 ×27^15 = 3^3x
X=?

Answer 1

GIVEN :–

$\\ \implies { \bold{ {9}^{18} \times {27}^{15} = {3}^{3x} }}$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

▪︎ We know that –

• 3¹ = 3

• 3² = 9

• 3³ = 27

▪︎ So we can write this as –

$\\ \implies { \bold{ { \{3}^{2} \}^{18} \times \{ {3}^{3} \}^{15} = {3}^{3x} }}$

▪︎Using identity –

$\\ \implies { \bold{ { \{a}^{b} \}^{c}= {a}^{bc} }}$

• So that –

$\\ \implies { \bold{ { \{3} \}^{36} \times \{ {3} \}^{45} = {3}^{3x} }}$

▪︎ Using identity –

$\\ \implies { \bold{ {a}^{b} .{a}^{c}= {a}^{b + c} }}$

$\\ \implies { \bold{ { \{3} \}^{36 + 45}= {3}^{3x} }}$

$\\ \implies { \bold{ { 3}^{81}= {3}^{3x} }}$

• Now compare –

$\\ \implies { \bold{ 3x = 81}}$

$\\ \implies { \bold{ x = \cancel \dfrac{ 81}{3}}}$

$\\ \implies \large { \boxed{ \bold{ x =27}}}$

Answer 2

${\boxed{\underline{\red{\sf{QUESTION :}}}}}$

${\sf{9 {}^{18} \: \times 27 {}^{15} = 3 {}^{3x} }}$

${\boxed{\underline{\blue{\sf{SOLUTION :}}}}}$

$\implies \: \sf9 {}^{18} \times 27 {}^{15} = 3 {}^{3x} \\ \implies \: \sf3 {}^{36} \times 3 {}^{45} = 3{}^{3x} \\ \sf \implies \: 3 {}^{(36 + 45)} = 3x \\ \implies \sf \: 3 {}^{81} = 3 {}^{3x} \\ \implies \sf \: 3 {}^{3x} = 3 {}^{81} \\ \implies \sf 3x \: = 81 \\ \implies \sf \: x \: = \frac{ \cancel{81}}{ \cancel{3}} \\ \implies \sf \: { \red{\boxed{ \rm x = 27}}}$

Therefore, the value of x is 27.

${\boxed{\green{\underline {\sf{Some\: \:Algebraic\: formulas :-}}}}}$

•a² – b²= (a – b)(a + b)

•(a+b)² = a² + 2ab + b²

•a² + b² = (a + b)² – 2ab

•(a – b)² = a² – 2ab + b²

•(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

•(a – b – c)² = a² + b² + c² – 2ab + 2bc – 2ca.

•(a + b)³ = a³ + 3a²b + 3ab² + b³