Question

1.Find the value of x in the equation below

3^(2x+1)÷3^(3x-4)×3^(6-7x)=27x

2.Solve the equation 2^(x+y)=8 and 3^(x-y)=1 simultaneously​

Answer 1

Explanation:

Hello, please consider the following.

Question 1.

`(3^(2x+1))/(3^(3x-4)\cdot 3^(6-7x))=27^x\\\\<=> 3^(2x+1)\cdot 3^(-3x+4)\cdot 3^(-6+7x)=3^(2x+1-3x+4-6+7x)=(3^3)^x=3^(3x)\\\\<=> 2x+1-3x+4-6+7x=3x\\\\<=> 6x-1=3x\\\\<=> 3x=1\\\\<=> \boxed{x=(1)/(3)}`

Question2.

`2^(x+y)=8=2^3 <=>x+y=3\\\\3^(x-y)=1=3^0<=>x-y=0`

So, it gives (by adding the two equations) 2x = 3

`\boxed{x=(3)/(2) \ \ and \ \ y = x = (3)/(2) }`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you