An inequality for a linear form in the logarithms of algebraic numbers

Let $\ln\alpha_1,\dots,\ln\alpha_{m-1}$ be the logarithms of fixed algebraic numbers which are linearly independent over the field of rational numbers, $b_1,\dots,b_{m-1}$ rational integers, $\delta>0$. A bound from below is deduced for the height of the algebraic number $\alpha_m$ under the condition that
$$ |b_1\ln\alpha_1+\dots+b_{m-1}\ln\alpha_{m-1}-\ln\alpha_m|<\exp\{-\delta H\}, \quad H=\max|b_k|>0. $$