Question

how to do this question​

Answer 1

Answer:

$x \: = \: 8$

Step-by-step explanation:

Given---->

${2}^{x - 7} \: \times {5}^{x - 4} \: = 1250$

To find---->

$value \: of \: x \:$

Concept used---->

1)

${a}^{m} \: \times {a}^{n} \: = {a}^{m + n}$

2)

$\dfrac{ {a}^{m} }{ {a}^{n} } \: = {a}^{m - n}$

3)

$( \: {a}^{m} \: ) ^{n} \: = {a}^{mn}$

4)

${a}^{0} = 1$

5)

${( \: ab \: )}^{m} = {a}^{m} \: {b}^{m}$

6)

$\sqrt[m]{a} \: = {a}^{ \frac{1}{m} }$

Solution--->

$we \: know \: that \\ 1250 \: = 5 \times 5 \times 5 \times 5 \times 2$

$now \:$

${2}^{x - 7} \times {5}^{x - 4} \: = 1250$

$= > {2}^{x - 7} \times {5}^{x - 4} = 5 \times 5 \times 5 \times 5 \times 2$

$= > {2}^{x - 7} \times {5}^{x - 4} = {5}^{1 + 1 + 1 + 1} \times 2$

$= > {2}^{x - 7} \times {5}^{x - 4} = {5}^{4} \times 2$

$comparing \: exponent \: of \: both \: sides \: we \: get \:$

$= > x - 4 = 4 \: \: or \: x - 7 = 1$

$= > x = 4 + 4 \: \: \: \: or \: x = 7 + 1$

$= > x = 8 \: \: \: \: or \: x = 8$

$it \: means \: value \: of \: x \: is \: 8$

$x \: = \: 8$