Log (base10) (x+1) - log (base10) (10x-3) = 1

Keep in mind: logarithmic definition a = log (base b) (b * * a) where * * is exponent and the fact that these logs are the same base (base 10)

Log (base10) (x+1) - log (base10) (10x-3) = 1

Log (base10) (x+1) - log (base10) (10x-3) + log (base10) (10x-3) = 1 + log (base10) (10x-3)

log (base10) (x+1) = 1 + log (base10) (10x-3)

since 1 = log (base 10) (10) since 10 = 10 * * 1

log (base10) (x+1) = log (base 10) (10) + log (base10) (10x-3)

log (base10) (x+1) = log (base10) (10 (10x - 3)) since all logs have same base of 10

x + 1 = 10 (10x - 3)

x + 1 = 100x - 30

-99x = - 31

x = - 31/-99 = 0.31