HELP? Complicated! How do I solve this

We're doing this in Elementary school right now? I need it for an exam tomorrow! Can you help me?

2^((3x-1)/3) = 16sqrt(8)

2^((3x-1)/3) =16sqrt(8)
=(2^4)sqrt(2^3)
=(2^4)(2^3)^(1/2)
=(2^4){2^(3/2)}
=2^{4+(3/2)}
=2^(11/2)

Thus,
2^((3x-1)/3)=2^(11/2)

Since a^m=a^n implies m=n, we have
(3x-1)/3 =11/2

Cross-multiplying,
2(3x-1)=3(11)
i.e., 6x-2=33
i.e., 6x=33+2=35

Thus, x=35/6 =5.8333

2^((3x-1)/3) = 16sqrt(8)

log[2^((3x-1)/3)] = log(16sqrt(8))

((3x-1)/3)*log 2 = log 16 + log sqrt 8

((3x-1)/3)*log 2 = log (2*2*2*2) + log sqrt (2*2*2)

((3x-1)/3)*log 2 = log (2*2*2*2) + log (2*sqrt (2))

Add logs to multiply things...

= 4*log 2 + log 2 + (1/2)*log 2

= 5.5*log 2
Dividing by log 2
(3x-1)/3 = 5.5

3*x - 1 = 16.5

x = 17.5/3 = 35/6 <<<

x = 5.83333