Question 151169
Solve for x:
{{{2log(x)-log(7) = log(112)}}} Apply the power rule for logs to the first term.
{{{log(x^2)-log(7) = log(112)}}} Now apply the quotient rule.
{{{log((x^2/7)) = log(112)}}} Apply the identity rule: If {{{log(a) = log(b)}}} then {{{a = b}}}
{{{x^2/7 = 112}}} Multiply both sides by 7.
{{{x^2 = 784}}} Take the square root of both sides.
{{{x = 28}}} Only the positve value of the square root is valid.
Check:
{{{2log(x)-log(7) = log(112)}}} Substitute x = 28.
{{{2log(28)-log(7) = log(112)}}}
{{{log((28^2/7))) = log(112)}}}
{{{log((784/7)) = log(112)}}}
{{{log(112) = log(112)}}}