Question

Find the value of x in 2 power(x-7) × 5 power(x-4) = 1250.

Answer 1

1250 = 5^4 × 2^1

according to the question,

x-7 = 1
x = 8

Answer 2

Answer:

Given :-

$\longrightarrow$ $\ 2^{x - 7} × \ 5^{x -4} = 1250$

Solution :-

$\longrightarrow$ $\ 2^{x - 7} × \ 5^{x - 4} = 1250$

$\Rightarrow$ $\ 2^{x - 7} × \ 5^{x - 4} = 2 × 5 × 5 × 5 × 5$

$\Rightarrow$ $\ 2^{x - 7} × \ 5^{x - 4} =\ 2^{1} × 5^{4}$

$\Rightarrow$ $x - 7 = 1$

$\Rightarrow$ $x = 1 + 7$

$\Rightarrow$ $x = 8$

Either,

$\Rightarrow$ $x - 4 = 4$

$\Rightarrow$ $x = 4 + 4$

$\Rightarrow$ $x = 8$

$\therefore$ $The\: value\: of\: x\: is\: 8$