Question 22212
Simplify:
{{{log(7,(5x)) - log(7,(x+3)) = 4log(7,(3))}}} Apply the Quotient rule for logarithms: {{{log(b,M)-log(b,N) = log(b,(M/N))}}} to the left side. The right side is rewritten because: {{{log(b,M^p) = p*log(b,M)}}}
{{{log(7,(5x/(x+3))) = log(7,(3^4))}}} If {{{log(b,M) = log(b,N)}}} then {{{M=N}}}, so:
{{{5x/(x+3) = 3^4}}}
{{{5x/(x+3) = 81}}} Multiply both sides by (x+3)
{{{5x = 81x + 243}}} Subtract 243 from both sides.
{{{5x-243 = 81x}}} Subtract 5x from both sides.
{{{-243 = 76x}}} Divide both sides by 76.
{{{x = -3.197368}}}