Question

Find value of x if (125/27) * (125/27)^x = (5/3)^18

Answer 1

Answer: x=5

Explanation:

`\displaystyle((125)/(27) )*((125)/(27) )^x=((5)/(3))^(18) \\\\((5^3)/(3^3))*((5^3)/(3^3))^x=((5)/(3))^(18)\\\\((5)/(3) )^3*(((5)/(3))^3)^x =((5)/(3))^(18)\\\\((5)/(3) )^3*((5)/(3))^(3*x)= ((5)/(3) )^(18)\\\\((5)/(3) )^3*((5)/(3))^(3x)= ((5)/(3) )^(18)\\\\((5)/(3))^(3x+3)= ((5)/(3) )^(18)\\\\Hence,\ \\\\3x+3=18\\\\3x+3-3=18-3\\\\3x=15\\\\`

Divide both parts of the equation by 3:

`x=5`