Consider the statement, 24 = . For what value of x is the statement true?
x=

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

⇒\sqrt{300c^9} =10c^x\sqrt{3c}

300c

9

=10c

x

3c

Squaring both sides we get;

(\sqrt{300c^9})^2= (10c^x\sqrt{3c})^2(

300c

9

)

2

=(10c

x

3c

)

2

Simplify:

300c^9 = 100c^{2x}(3c)300c

9

=100c

2x

(3c)

We know: a^m \cdot a^n = a^{m+n}a

m

⋅a

n

=a

m+n

then;

300c^9 = 300c^{2x+1}300c

9

=300c

2x+1

Divide both sides by 300 we get;

c^9 = c^{2x+1}c

9

=c

2x+1

On comparing both sides we have;

9 = 2x+19=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 4