Answer to Q143
2ˣ + 2ˣ⁻¹ = 6144. Find x
This is eqn i: 2ˣ + 2ˣ⁻¹ = 6144
eqn i can be rewritten as:
2ˣ + (2ˣ ÷ 2) = 6144 eqn ii
2ˣ (1 + ½) = 6144
2ˣ (³⁄₂) = 6144 eqn iii
divide eqn iii through by ³⁄₂
2ˣ = 6144 ÷ ³⁄₂
2ˣ = 6144 x ⅔
2ˣ = 4096
logarithm rule comes in here
log⁴⁰⁹⁶ ÷ log² = x
x = 12
Answer: 12
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