Question

I am once again in need of mathematical guidance

Answer 1

a=-3

b=5/2

c=-1/2

Explanation:

3^-3=1/3^3=1/27 a=-3

3^5/2=√3^5=9√3 b=5/2

3^-1/2=1/√3 c=-1/2

Answer 2

1. a = -3
2. b = 5/2
3. c = -1/2

Explanation:

`3^b = 9√(3) \\Convert 9√(3) to base 3\\ 3^b = 3^{(5)/(2) } \\Cancel-out-the-base\\b = 5/2`

`3^c = (1)/(√(3) ) \\Apply -exponent -rule ;(1)/(a^b)=a^(-b)\\(1)/(√(3))=3^{-(1)/(2)}\\3^c = 3^{-(1)/(2) } \\\mathrm{Apply\:exponent\:rule}:\quad \sqrt[n]{a}=a^{(1)/(n)}\\3^{-(1)/(2)}=3^{-(1)/(2)}\\3^c = 3^{-(1)/(2) } \\\mathrm{If\:}a^(f\left(x\right))=a^(g\left(x\right))\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)\\c = -(1)/(2)`

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