If 1- ₁₀2= ₁₀(5^x+4^x+3^x+2^x+1) , then what is a value of x ?

Step-by-step solution

The given equation is 1 - ₁₀2 = ₁₀(5^x + 4^x + 3^x + 2^x + 1) Simplifying the left hand side: 1 - ₁₀2 = ₁₀10 - ₁₀2 = ₁₀ ( 10 2 ) = ₁₀5 Equating this to the right hand side: ₁₀5 = ₁₀(5^x + 4^x + 3^x + 2^x + 1) Since the logarithmic function is one-to-one, we can equate the arguments: 5 = 5^x + 4^x + 3^x + 2^x + 1 5^x + 4^x + 3^x + 2^x = 4 Substituting x = 0 into the equation: 5^0 + 4^0 + 3^0 + 2^0 = 1 + 1 + 1 + 1 = 4 Thus, x = 0 satisfies the equation. Answer: 0