Question 689611
Solving equations where the variable is in the argument of a logarithm usually starts with transforming the equation into one of the following forms:
log(expression) = number
or
log(expression) = log(expression)<br>
You equation, 4 = ln(x+5), is already in the first form. The next step with this form is to rewrite the equation in exponential form. In general {{{log(a, (p)) = q}}} is equivalent to {{{a^q = p}}}. Using this patter on your equation (and the fact the the base of ln is e):
{{{e^4 = x + 5}}}
Now we just subtract 5 from each side:
{{{e^4 - 5 = x }}}
This is an exact expression for the solution to your equation. If you want/need a decimal approximation then just use your calculator to evaluate the left side. (If your calculator does not have a button for the number "e", then use 2.7182818284590452353602874713527 (or some rounded off version of this).)