log a base b ×log b base a =1
Answers
The equation is true for all values of b and a, as long as they are both positive and not equal to 1.
There are four following math logarithm formulas: ● Product Rule Law:
loga (MN) = loga M + loga N. ● Quotient Rule Law:
loga (M/N) = loga M - loga N. ● Power Rule Law:
IogaMn = n Ioga M. ● Change of base Rule Law:To solve the equation log_b(log_a(b)) = 1, we can use the definition of logarithms and some basic algebraic manipulations:
log_b(log_a(b)) = 1
This equation can be rewritten using the change-of-base formula:
log_a(b) / log_a(b) = 1
Simplifying the left-hand side, we get: 1 = 1
Therefore, the equation is true for all values of b and a, as long as they are both positive and not equal to 1.
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