Question

26 x 23 ÷ 24 = 2x then x is equal to
a) 2
b) 3
c) 5
d) 7​

Answer 1

Given :  2⁶ x 2³  ÷  2⁴  = 2ˣ

To Find :  x

a) 2

b) 3

c) 5

d) 7​

Solution:

Law of exponents :

 a , b are non zero integers   m, n are integers

$\begin{align} & {{\text{a}}^{n}}\times {{a}^{-n}}=1\text{ or }{{\text{a}}^{n}}=\frac{1}{{{a}^{n}}} \\ & {{a}^{m}}\times {{a}^{n}}={{a}^{m+n}} \\ & \frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}} \\ & {{\left( {{a}^{m}} \right)}^{n}}={{\left( {{a}^{n}} \right)}^{m}}={{a}^{mn}} \\ & {{a}^{m}}\times {{b}^{m}}={{\left( ab \right)}^{m}} \\ & \frac{{{a}^{n}}}{{{b}^{n}}}={{\left( \frac{a}{b} \right)}^{n}}$

a⁰ = 1

2⁶ x 2³  ÷  2⁴  = 2ˣ

=> 2⁶⁺³ ÷  2⁴  = 2ˣ

=> 2⁹ ÷  2⁴  = 2ˣ

=> 2⁹⁻⁴ = 2ˣ

=> 2⁵ = 2ˣ

Equate powers as base are equal

=> 5 = x

=> x = 5

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