Question

2 raise to power x into 5 raise to power x=10000 find x

Answer 1

2^x * 5^x = 10000
(2*5)^x=10000
10^x=10000
10^x=(10)^4
Therefore, x=4

Answer 2

$\textbf{Answer}$

Given question can be written as,

2^x × 5^x = 10000

We know that,
a^x × b^x = (a×b)^× -----------(1)
10000 = 10^4 ------------------(2)

=> 2^x × 5^x = 10000

$\textbf{Using equation (1),}$
=> (2×5)^x = 10000

$\textbf{Using equation (2),}$
(10)^x = 10^4 ------(3)

Now comparing LHS & RHS of equation (3),

x = 4

So the value of x is 4

$\textbf{Hope It Helps}$

$\textbf{Thanks}$