Solve for b if: 4log base2 2x + 2log base b x = 4

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