If ₁₀ 2, ₁₀ (2^x-1 ), ₁₀ (2^x+3 ) are in AP, then what is x equal to?

Step-by-step solution

aligned & _ 10^2 , ₁₀ (2^x-1 ), ₁₀ (2^x+3 ) are in A.P. & ₁₀ (2^x-1 )= ₁₀ 2^2+ ₁₀ (2^x+3 ) & ₁₀ (2^x-1 )^2= ₁₀ (2^x+3 ) & (2^x-1 )^2=2 (2^x+3 ) & (2^x )^2-2.2^x+1=2.2^x+6 & (2^x )^2-4.2^x-5=0 & (2^x-5 ) (2^x+1 )=0 & 2^x+1 0 & 2^x-5=0 & 2^x=5 & x= ₂ 5 aligned