Question 271271
To solve logarithmic equations where the variable is in the argument, you want to start by geeting the equation into one of the following forms:
log(variable-expression) = other expression
or
log(variable expression = log(other-expression)<br>
We can achieve the first form by subtracting two from each side:
{{{ln(x-3) = 8}}}
And now that the equation is in the first form, we proceed by rewriting the equation in exponential form:
{{{x-3 = e^8}}}
By rewriting the equation in exponential form we have extracted the variable from the argument of a logarithm. We can now solve for x by adding 3 to each side:
{{{x = e^8 + 3}}}
This is an exact answer for the problem. If you want a decimal approximation you can use your calculator on the right side. (If your calculator does not have a button for e, use 2.7182818284590452353602874713527 (or some rounded-off version of this number).