Question 381355
2ln(4x)=15
With a variable in the argument of a logarithm, you usually start by transforming the equation into one of the following forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)<br>
All we have to do to your equation to reach the first form is to divide by 2:
{{{ln(4x) = 15/2}}}
With the first form, the next step is to rewrite the equation in exponential form. In general {{{log(a, (p)) = q}}} is equivalent to {{{p = a^q}}}. Using this on your equation we get:
{{{4x = e^(15/2)}}} (Since e is the base of ln.)
And last of all, we multiply by 1/4. (Dividing by 4 works, too.)
{{{x = (1/4)e^(15/2)}}}
This is an exact expression for the solution to your equation.