log10x + log10(x+1)=1

Question

In other words
log base 10 + log base 10(x+1)=1

I need to show it algebraically not using calculator

Thanks a lot !

Answer 1

log10x + log10(x+1)=1
log10[x(x+1)] = 1
x(x+1) = 10^1
x^2 + x - 10 = 0
x = (-1 ± √41)/2

but for log10 x, x > 0

so x = (-1 + √41)/2

Answer 2

thanks for you help and especially explanation