A Wonderful Math Olympiad Exponential Problem

[@ExploredMaths]

Thanks for step by step solution😊

[@pspprabhat]

2^3×=3(2^4)
=>(3×)log2 =log3+4log2
=>(3×-4)=log3/log2
=>×=( 1/3{4+log@2(3)}
=1.33+0.4771/3(0.03)
=1.85

[@sie_khoentjoeng4886]

8^X = 48
Log 8^X = Log 48
X = Log 48 / Log 8
X = Log (8*6) / Lig8
X = Log 8 / Log 8 + Log 6 / Log 8
X = 1 + Log6 / Log8

[@walterwen2975]

A Wonderful Math Olympiad Exponential Problem: 8ˣ = 48; x = ?
8ˣ = 2³ˣ = 48 = 3(16) = 3(2⁴), Let: 3 = 2ᵃ; a = log₂3 = 1.585, 2¹·⁵⁸⁵ = 3
2³ˣ = 3(2⁴) = (2¹·⁵⁸⁵)(2⁴) = 2⁵·⁵⁸⁵; 3x = 5.585, x = 5.585/3 = 1.862
Answer check:
8ˣ = 8¹·⁸⁶² = 48; Confirmed
The calculation was achieved on a smartphone with a standard calculator app
Final answer:
x = 1.862

[@RealQinnMalloryu4]

6^8 3^2^2^3 3^12^1 32 (x ➖ 3x+2)