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

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

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.