United States l can you solve this?? l Nice Olympiad Math Exponential Problem l K=?

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2^(k+2)+2^(K-1)=15 common factor 2^(K-1) on LHS
2^(K-1)(2^3+1)=15 divide by 9 (2^3+1)
2^(K-1)=5/3 log on both sides
(K-1)log(2)=log(5)-log(3) solve for K
K=1+(log(5)-log(3))/log(2) change to logarithm base 10
K=(1-log₁₀(3))/log₁₀(2)=1.73696559416621 (approx.)