Question

Find the value of x when 9^18 × 27^15 = 3^3x ​

Answer 1

$\sf\large\underline\blue{Given:-}$

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

$\sf\large\underline\blue{To\: Find :-}$

• Value of x

$\sf\large\underline\blue{Formula\: used:-}$

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

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

$\sf\large\underline\blue{Solution:-}$

Given that,

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

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

As we know that,

( 3¹ = 3 , 3² = 9, 3³ = 27 )

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

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

$↦ { \bold{ { 3}^{81}= {3}^{3x} }}$

__________________________________________________

After comparing, we get

$↦{ \bold{ 3x = 81}}$

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

$↦{ \bold{ x = 27}}$

$\small{\underline{\sf{\blue{Hence-}}}}$

Value of x is = 27

Answer 2

Answer:

27

Step-by-step explanation:

I hope it is correct answer