Question 70985
Try this!
Apply the qoutient rule for logarithms:{{{Log(M)-Log(N) = Log(M/N)}}}
{{{Log[2](5x+7)-Log[2](x) = Log[2]((5x+7)/x)}}}, so now you have:
{{{Log[2]((5x+7)/x) = 2}}} Rewrite this in exponential form:
{{{2^2 = (5x+7)/x}}}
{{{4 = (5x+7)/x}}} Multiply both sides by x.
{{{4x = 5x+7}}} Subtract 5x from both sides.
{{{-x = 7}}} Multiply both sides by -1.
{{{x = -7}}}
Check:
{{{Log[2]((5x+7)/x) = 2}}} Substitute x = -7.
{{{Log[2](((5(-7)+7))/(-7)) = 2}}} Simplify.
{{{Log[2](-28/-7) = 2}}}
{{{Log[2](4) = 2}}} Change the base from 2 to 10.
{{{Log[2](4) = (Log[10](4))/Log[10](2)}}} Evaluate using your calculator or log tables.
{{{(Log[10](4))/(Log[10](2)) = 2}}}