Question 404441
ln(5x+20)=2
Solving equations where the variable is in the argument of a logarithm, like this equation, usually starts with transforming the equation into one of the following forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)<br>
Your equation is already in the first form. So we can proceed to the next step, which is to rewrite the equation in exponential form. In general {{{log(a, (p)) = q}}} is equivalent to {{{p = a^q}}}. Using this pattern on your equation (and using the fact that the base of ln is "e") we get:
{{{5x+20 = e^2}}}
We can now solve for x. Subtracting 20 from each side we get:
{{{5x = e^2 - 20}}}
Dividing by 5 we get:
{{{x = (e^2 - 20)/5}}}
This is an exact expression of the solution to your equation. You are asked to find a decimal (approximation). So get out your calculator. (If your calculator does not have a button for the number "e", use 2.7182818284590451 (or some rounded off version of it).)