Question

how to find x : log10(x+6)-log10(x-3)=1

Answer 1

Condense first:
\[\log _{10}(x+6)-\log _{10}(x-3) = \log _{10} [(x+6)/(x-3)]\] Since that is = 1, we can rewrite in exponential form and see that \[10^{1}=[(x+6)/(x-3)]\] Multiplying both sides by x-3 will yield a linear equation with 10x-30=x+6 and, solving for x, 9x=36 and this yields the answer x=4. Checking it in the equation verifies it is a solution.