log8x

log8x is a logarithmic function where the base of the logarithm is 8. It is the inverse function of the exponential function 8^y. This means that if log8x = y, then 8^y = x. The function log8x is defined for all positive values of x. The value of log8x represents the power to which 8 must be raised to obtain x. For example, log8(64) = 2 because 8^2 = 64.

The domain of log8x is (0, infinity), meaning x must be a positive real number. The range of log8x is (-infinity, infinity), meaning the output can be any real number. The graph of y = log8x passes through the point (1, 0) because any base logarithm of 1 is 0. As x approaches 0 from the positive side, log8x approaches negative infinity. As x increases, log8x also increases, but at a decreasing rate.

Logarithms with base 8 can be converted to other bases, such as base 10 or the natural logarithm (base e), using the change of base formula. For instance, log8x can be written as log(x) / log(8) or ln(x) / ln(8). This property is useful for calculations and for understanding the behavior of log8x in relation to other logarithmic functions.