Question 21784
Solve for x:
{{{log((2+x)) - log(x) = log(11)}}} Apply the Quotient rule for logarithms to the left side. {{{log(M) - log(N) = log((M/N))}}}
{{{log(((2+x)/x)) = log(11)}}} If log a = log b, then a = b
{{{(2+x)/x = 11}}} Multiply both sides by x.
{{{2+x = 11x}}} Subtract x from both sides.
{{{2 = 10x}}} Divide both sides by 10.
{{{x = 2/10}}}
{{{x = 0.2}}}

Check: Use your calculator or a table of logarithms to find the values of the logs.

{{{log((2+0.2)) - log(0.2) = 1.04139}}}
{{{log(11) = 1.04139}}}