There are two logarithm concepts that are not in the usual
textbooks, guides or ten years series. However, these two concepts
are already known to students and teachers.
Question
(1) Evaluate logn 9 / logn 4
(2) Given that zy = 2^[log2 (z + x)], show that z = x / [y-1]
[The number or letter in red is in subscript ie the base of the
log].
These two questions are not dificult as these two questions are
just used to illustrate the two logarithm concepts where some
students might not be aware.
The concept used in question 1 is
logn 9 / logn 4 = ratio of the logarithms of any same
base ie
logn 9 / logn 4 = log10 9 / log10 4 = loge 9 / loge 4 = log2 9 / log2 4 and so on.
The concept used in the second question is
a^loga y = y.
So, 2^[log2 (z + x)] = z +
x, 3^ (log3 4) = 4, e^ (ln
x^2) = x^2, 10^ (lg 7) = 7 and so on
[The number or letter in red is in subscript ie the base of the
log].
Third Concept
With the ratio of the logarithm of any same base,
logn 3 / logn 2
= log2 3
Answer for Question
1
logn 9 / logn 4 = log10 9 / log10 4 = 1.585
Answer for Question
2
zy = 2^[log2 (z + x)]
zy = z + x
zy - z = x
z(y - 1) = x
z = x/(y - 1) (shown)