SOLUTION: How do you solve this equation? 4=ln(x+5) thank you

Question 689611: How do you solve this equation? 4=ln(x+5)
thank you
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
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)

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 is equivalent to . Using this patter on your equation (and the fact the the base of ln is e):

Now we just subtract 5 from each side:

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).)

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