If 2log10( x+1 ) = log10( 7x+1 ), then find the non zero value of X ?

Solution: Use the logarithm power rule to combine the left-hand side.

2·log10(x+1) = log10(7x+1) ⇒ log10((x+1)^2) = log10(7x+1)

Therefore (x+1)^2 = 7x+1.

• Expand and simplify: x^2 + 2x + 1 = 7x + 1 → x^2 − 5x = 0.

• Factor: x(x − 5) = 0, so x = 0 or x = 5.

The question asks for the non-zero value, so choose x = 5. Check domain: x > −1 is required for the logarithms, and x = 5 satisfies this.