SOLUTION: solve for x to the nearest thousandth: ln(5x+20)=2

Question 404441: solve for x to the nearest thousandth: ln(5x+20)=2
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
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)

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 is equivalent to . Using this pattern on your equation (and using the fact that the base of ln is "e") we get:

We can now solve for x. Subtracting 20 from each side we get:

Dividing by 5 we get:

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).)
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