Question 607251
{{{5+8*ln(x)=25.8}}}
Solving equations where the variable is in the argument (or base) of a logarithm usually starts by using algebra and/or log properties to transform the equation into one of the following forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)<br>
Your equation, with its single logarithm, should be transformed into the first form. This can be done quite simply. Subtract 5 from each side:
{{{8*ln(x) = 23.8}}}
Then we divide both sides by 8:
{{{ln(x) = 23.8/8}}}
which simplifies to
{{{ln(x) = 2.975}}}<br>
The next step. with the first form, is to rewrite the equation in exponential form. In general, {{{log(a, (p)) = q}}} is equivalent to {{{a^q = p}}}. Using this pattern, and the fact that the base of ln is e, we get:
{{{e^2.975 = x}}}<br>
The next step is to solve for the variable. Your equation is already solved for the variable! All that is left, since a rounded decimal was requested, is to use your calculator:
{{{x = e^2.975 = (2.71828183)^2.975 = 19.59}}}