# Logs in an A.P.

Algebra Level 3

For $$x = \log _{ a }{ b }$$ the three numbers $$\log _{ 10 }{ 2 }$$ , $$\log _{ 10 }{ ({ 2 }^{ x } } -1)$$ and $$\log _{ 10 }{ ({ 2 }^{ x } } +3)$$ form an arithmetic progression.

What is the value of $$(a+b)^{3}$$ ?

×