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## Main Question or Discussion Point

A simple doubt came to my mind while browsing through logarithmic functions and natural logarithms

we define

$$\log_b(xy) = \log_b(x) + \log_b(y)$$

Here

why is the condition imposed that b>1 and b is not equal to zero and that x and y are positive numbers?

Is it something to do with the function being continuous and monotonically increasing or decreasing in certain intervals(1,infinity) and (0,1) respectively?

UchihaClan13

we define

$$\log_b(xy) = \log_b(x) + \log_b(y)$$

Here

why is the condition imposed that b>1 and b is not equal to zero and that x and y are positive numbers?

Is it something to do with the function being continuous and monotonically increasing or decreasing in certain intervals(1,infinity) and (0,1) respectively?

UchihaClan13