Please explain the difference between log and LG and LN, as well as their formulas,

Log is the logarithm sign. The photo number and base number on the right (the top is the real number and the bottom number below) are abbreviated as LG when the base number is 10 and LN when the base number is e. for example, LN5 is the logarithm with E as the base and 5 as the real number

What if the log base is 2 and the true number is 1 / 2?

1 / 2 = 2 ^ (- 1) get - 1 according to the property of logarithm

What is the log base 2 and the true number 8?

Log2 8 = log2 (the third power of 2) = 3

Calculate 2 ^ log (1 / 4) 3 =? (1 / 4 is the base number and 3 is the real number) Calculation process, thank you!

2 ^ log (1 / 4) 3 = 2 ^ [log (2) 3 / log (2) 1 / 4] = 2 ^ [log (2) 3 / - 2] = 2 ^ log (2) 3 ^ (- 1 / 2) = 3 ^ (- 1 / 2) = root 3 / 3
perhaps
Original formula = [(1 / 4) ^ (- 1 / 2)] ^ log (1 / 4) 3 = 3 ^ (- 1 / 2) = - root sign 3 / 3

Logarithmic solution equation log2 (x-1) - log4 (x + 2) + 1 = 0 2 and four are true numbers in the bottom bracket

log2(x-1)-log4(x+2)+1=0
(x-1)^2/(x+2)=1/4
After sorting, x ^ 2-2.25x + 1.5 = 0
X = 0.25 or 2
Through inspection, it is found that x = 0.25 does not meet the meaning of the question, and x = 2 meets the meaning of the question
So, x = 2

In the operation of logarithm, there are several derived formulas. One is log (a) (b) * log (b) (a) = 1. How do you get it? I did it with the bottom - changing formula, but the teacher spoke too fast and I didn't understand The first parenthesis after log is the base number, and the second is the true number

Log (a) (b) can be written in the same way after LGB / LGA. Log (b) (a) = LGA / LGB, so multiplying the two is 1
Do you understand

Please explain the difference between log and LG and LN, as well as their formulas,