Question

Consider the statement square root 300c^9 = 10c^x square root 3 c

For what value of x is the statement true
X=??

Answer 1

Given the statement: Square root 300c^9 = 10c^x square root 3 c

⇒
`√(300c^9) =10c^x√(3c)`

Squaring both sides we get;

`(√(300c^9))^2= (10c^x√(3c))^2`

Simplify:

`300c^9 = 100c^(2x)(3c)`

We know:
`a^m \cdot a^n = a^(m+n)`

then;

`300c^9 = 300c^(2x+1)`

Divide both sides by 300 we get;

`c^9 = c^(2x+1)`

On comparing both sides we have;

`9 = 2x+1`

Subtract 1 from both sides we get;

8 = 2x

Divide both sides by 2 we have;

x = 4

Therefore, for the value of x =4 the given statement is true.