Abstract For an integer $$k\ge 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>k</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> , let $$L^{(k)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:math> be the k –generalized Lucas sequence which starts with $$0, \ldots , 2,1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> (a total of k terms) and for which each term afterwards is the sum of the k preceding terms. In this paper we assume that an integer c can be represented in at least two ways as the difference between a k –generalized Lucas number and a power of b , then using the theory of nonzero linear forms in logarithms of algebraic numbers, we bound all possible solutions on this representation of c in terms of b . Finally, combination our general result and some known reduction procedures based on the continued fraction algorithm, we find all the integers c and their representations for $$ b\in [2,10]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>b</mml:mi><mml:mo>∈</mml:mo><mml:mo>[</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>10</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:math> , this argument can be generalized to any $$ b&gt; 10 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>b</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:math> .