Question

2^x-4 . 5^2x-13=100000.find x

Answer 1

Answer:

The value of x is 9

Step-by-step explanation:

$2^{x-4}.5^{2x-13}=100000$

$2^{x-4}.5^{2x-13}=10^5$

$2^{x-4}.5^{2x-13}=(2*5)^5$

$2^{x-4}.5^{2x-13}=2^5*5^5$

Equating the powers, we get

x-4=5

x=9

2x-13=5

2x=18

x=9

The value of x is 9

Answer 2

Answer:

x = 9

Step-by-step explanation:

2^x-4 . 5^2x-13=100000.find x

2ˣ⁻⁴ * 5²ˣ⁻¹³ = 100000

=> 2ˣ⁻⁴ * 5²ˣ⁻¹³ = 10⁵

10 = 2 * 5

=> 2ˣ⁻⁴ * 5²ˣ⁻¹³ = (2 * 5)⁵

as we know that (a * b)ⁿ = aⁿ * bⁿ

so (2 * 5)⁵ = 2⁵ * 5⁵

=> 2ˣ⁻⁴ * 5²ˣ⁻¹³ = 2⁵ * 5⁵

as 2 & 5 are co-prime so 2ˣ⁻⁴ & 5²ˣ⁻¹³ are independent and does not have any factor

=> 2ˣ⁻⁴ = 2⁵

&  5²ˣ⁻¹³  = 5⁵

nᵃ = nᵇ => a = b using this

x-4 = 5 => x = 9

or 2x - 13 = 5 => x = 9

Hence x = 9 if 2ˣ⁻⁴ * 5²ˣ⁻¹³ = 100000