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Mathematics
Daniel Huerta
2 May, 21:51
Solve for b if: 4log base2 2x + 2log base b x = 4
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Tony Clements
3 May, 00:03
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Log base b=logb
4 log₂ 2x + 2logb x=4
log₂ (2x) ⁴+logb x²=log₂16
log₂ 16x⁴ + logb x²=log₂ 16
logb x²=log₂ 16 - log₂ 16x⁴
logb x²=log₂ (16/16x⁴)
logb x² = log₂ x⁻⁴
logb x²=log₂ x² / log₂ b
log₂ x² / log₂ b=-log x⁴
log₂ b=log₂ x² / - log₂ x⁴
log₂ b=2 log x / - 4 log₂ x
log₂ b=-1/2 ⇔ b=2⁻¹/² = 1/√2 = (√2) / 2≈ 0.707106781 ...
Answer: b = (√2) / 2
To chek
if x=10
log base √2/2 = log√2/2
4 log₂ 20 + 2log√2/2 10=4 (4.321928095 ...) + 2 (-6.64385619=
= 17.28771238-13.28771238=4
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