Write a number in the box. This can be a fraction like 1/2, or a number like 4 or 0.5. But the answer has to be exact, so you cannot use 0.33 to mean 1/3.
\large{\log_{BASE}} EXP < 0 ? "\\left(" + NUM_STR + "\\right)" : NUM_STR = \text{?}
EXP
If b^y = x, then \log_{b} x = y.
Therefore, we want to find the value y such that BASE^{y} = NUM_STR.
Any number raised to the power 1 is simply itself, so BASE^{1} = BASE and thus \log_{BASE} BASE = 1.
Any non-zero number raised to the power 0 is simply 1, so BASE^0 = 1 and thus \log_{BASE} 1 = 0.
Any number raised to the power -1 is its reciprocal, so BASE^{-1} = \dfrac{1}{BASE} and thus \log_{BASE} \left(\dfrac{1}{BASE}\right) = -1.
In this case, BASE^{EXP} = NUM_STR,
so \log_{BASE} \left(NUM_STR\right) = EXP.
In this case, BASE^{EXP} = NUM_STR,
so \log_{BASE} NUM_STR = EXP.
Write a number in the box. This can be a fraction like 1/2, or a number like 4 or 0.5. But the answer has to be exact, so you cannot use 0.33 to mean 1/3.
\large{\log_{NUM}} BASE = \text{?}
1/EXP
If b^y = x, then \log_{b} x = y.
Notice that BASE is the ["square", "cube", "fourth", "fifth"][EXP - 2] root of NUM.
That is, \sqrt{NUM} = NUM^{1/EXP} = BASE.
That is, \sqrt[EXP]{NUM} = NUM^{1/EXP} = BASE.
Thus, \log_{NUM} BASE = \dfrac{1}{EXP}.