The univariate Toppleone distribution introduced by [12] with close forms of cumulative distribution function i.e [0, 1] is extended to unbounded limit called Log-Toppleone distribution, the shapes of the hazard function can be increase, decrease or constant, therefore, can serve as an alternative distribution to the gamma, Weibull and exponential distributions. Bivariate of this proposed distribution is introduced by joining probability density function using three distinct copulas. The MLE, IFM and Bayesian method of estimation were employed to estimate the parameters, the Plackett copula regarded as the best based on MLE and IFM method of estimation while Clayton copula regarded as the best using Bayesian method.