Question 1149546

Remember the basic definition of a logarithm: "The logarithm of a number (5x-2) is the power (2) to which the base (e) must be raised to equal the number", so we can express this as:
{{{ln(5x-2) = 2}}} ---> {{{e^2 = (5x-2)}}} 

Now we can solve for x.
{{{e^2 = 5x-2}}}.......... Add {{{2}}} to both sides.
{{{e^2+2 = 5x}}}......... Divide both sides by {{{5}}}.
{{{x=(1/5) (e^2+2)}}}->exact answer
which
{{{x = 1.8778}}} ->approximately.