A Nice Olympiads Exponential Mathematics | How to Solve for k?

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[@SidneiMV]

2ᵏ = k³²
kln2 = 32lnk
(1/k)lnk = (1/32)/ln2
(1/k)ln(1/k) = (1/32)/ln(1/2)
(1/k)ln(1/k) = (1/2⁵)(1/2³)8ln(1/2)
(1/k)ln(1/k) = (1/2⁸)ln(1/2⁸)
*k = 2⁸*

[@SidneiMV]

another way
2ᵏ = k³²
(2ᵃ)ᵏ= k³²ᵃ
2ᵃ = 32a = k
2ᵃ⁻⁵ = a => a = 8 (by inspection)
*k = 2⁸*

[@SidneiMV]

another way
2ᵏ = k³²
(2⁸)ᵏ= (k³²)⁸
(2⁸)ᵏ= k^2⁸
*k = 2⁸*