Let’s see 96 = 2^6 + some change = 96/64 or 1.5 so 8^2 X 1.5 Log 8 of 1.5 = So log8 4 is 0.666 and log8 of 2 is .3333 and 1 is 0 This puts the answer somewhere between above .16667 and less than 0.333 Therefore 8^2.20 ~ 96. However, this is not the only answer as there are likely two more complex numbers that might also give the same answer. The better solution is ln (96)/ln(8) = 2.195
Let’s see 96 = 2^6 + some change = 96/64 or 1.5 so 8^2 X 1.5
Log 8 of 1.5 = So log8 4 is 0.666 and log8 of 2 is .3333 and 1 is 0
This puts the answer somewhere between above .16667 and less than 0.333
Therefore 8^2.20 ~ 96. However, this is not the only answer as there are likely two more complex numbers that might also give the same answer.
The better solution is ln (96)/ln(8) = 2.195
8^x=(2^3)^x=2^3x, 96=3*32=3*2^5, then 2^3x=3*2^5, 2^(3x-5)=3, (3x-5)log2=log3, x=(Log2(3)+5)/3