+plus (−minus) ↺ ·times (/over) ↺ ˄to (˅root ⍻log)
① 1⍻b = 0 ② b⍻b = 1 ③ (b˄x)⍻b = x ④ b˄(x⍻b) = x ⑤ (x˄p)⍻b = p·(x⍻b) ⑥ x⍻b = (x⍻c)/(b⍻c) ⑦ (x·y)⍻b = x⍻b+y⍻b ⑧ (x/y)⍻b = x⍻b-y⍻b
41 Logarithms Part 1
When we say log base b of x equals y, we are saying b to the y equals x.
With logs, the base of the log raised to the power of what's on the other side of the equal sign will equal the number that the log is operating on.
Change of base
Log base b of n.
What power should I put in the exponent of b so b to that power will give me n.
b˄n is called "b raised to the n-th power", "b raised to the power of n", "the n-th power of b", "b to the n-th", or most briefly as "b to the n"
"the log, base b, of x"
"To what power must b be raised, in order to yield x?"
In the same way that division is the inverse of multiplication a logarithm is just the inverse of exponentiation.
Anytime you see log base b of some number n, you can think about it as asking the question "What power do I need to put in my exponent to get b to that power equal to this number n?"
ᐥWhat power do you have to raise b to in order to get x?ᐥ