Question 73838
Solve:
{{{Log(x+11) - Log(x) = 3}}} Apply the quotient rule for lagarithms: {{{Log(M)-Log(N) = Log(M/N)}}}
{{{Log((x+11)/x) = 3}}} Rewrite this in exponential form.
{{{10^3 = (x+11)/x}}} Simplify and solve for x.
{{{1000 = (x+11)/x}}} Multiply both sides by x.
{{{1000x = x+11}}} Subtract x from both sides.
{{{999x = 11}}} Divide both sides by 999.
{{{x = 11/999}}} = 0.011011...This is a repeating decimal.