Question

$5 \sqrt{5} \times {5}^{3} + {5}^{ \frac{ - 3}{2} } = {5}^{ \frac{ - 3}{2} } ( {5}^{x + 2} + 1)$
Find x in this equation.​

Answer 1

Answer:

3x+5

−

6

5x−7

=

3

x−2

5×6

6(3x+5)−5(5x−7)

=

3

x−2

30

(18x+30)−(25x−35)

=

3

x−2

30

18x+30−25x+35

=

3

x−2

⇒3(65−7x)=30(x−2)

⇒195−21x=30x−60

⇒30x+21x=195+60

⇒51x=255

⇒x=

51

255

=5

Thus x=5