Question

if 9^x-9^x-1=24, then find the value of (6x)^x

Answer 1

That equation cannot possibly be true because :
\[9^x-9^x=0\]
and 0-1=24 can never be true for any value of x.

Answer 2

actually it CAN!!
not really.

Answer 3

Well, maybe if you used the premise that the reflexive axiom was invalid.

Answer 4

First find \(x\):
\[\begin{array}{rcl}
9^x-9^{x-1}&=&24\\
9^x-\frac{9^x}{9}&=&24 \\
\frac{8}{9}9^x&=&24 \\
9^x &=& \frac{9\cdot 24}{8}\\
9^x &=& 9\cdot \sqrt{9} \\
x&=& \frac{3}{2}
\end{array}
\]

Then plug it into \((6x)^x\)\[
\begin{split}
(6x)^x &= \left( \frac{6 \cdot 3}{2} \right)^{3/2} \\
&=9^{3/2}\\
&= 27
\end{split}
\]