SOLUTION: please help me solve this problem ln (x+5)

SOLUTION: please help me solve this problem ln (x+5) - ln (x-2) = 2 x= ??

Question 689681: please help me solve this problem
ln (x+5) - ln (x-2) = 2
x= ??
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
ln(x+5) - ln(x-2) = 2
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)

If we can find a way to combine the two logs into one the equation will be in the first form. The two logs are not like terms so we cannot just subtract them. (Like logarithmic terms have the same bases and the same arguments. Your logs have the same base, e, but the arguments, x+5 and x-2, are different.) Fortunately there is a property of logarithms that allow us to combine two logs with a "-" between them: . This property requires the same bases and coefficients of 1. Your logs meet both requirements. Using this property we get:

We now have the equation 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 that the variable is out of the logarithms we can solve for it. We'll start by multiplying each side by x-2 to eliminate the fraction:

Next we'll gather the x terms on one side and the other terms on the other side of the equation. Subtracting x and adding :

Factoring out x on the left side:

And finally divide both sides by

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 right side. (If your calculator does not have a button for the number "e", then use 2.7182818284590452353602874713527 (or some rounded off version of this).)
RELATED QUESTIONS
-could you please help me in this problem solve for x: ln(x-1)=ln(x-2)-ln... (answered by josgarithmetic)

Can you please help me with this equation? ln(x-5)-ln(x+4)=... (answered by scott8148)

Solve ln(3x+8)=ln(2x+2)+ln(x-2) for x Please help... (answered by khwang)

Hi, pleas help me solve this problem: Use logarithms to solve the equation... (answered by Alan3354)

please help me solve this problem express the equation in exponential form.... (answered by Alan3354)

Please help me with this natural log problem:... (answered by josgarithmetic)

please help me to solve this logarithmic : Ln x = 1/2 Ln (2x + 5/2) + 1/2 Ln 2 (answered by jsmallt9)

hello Could anyohne please help me solve this problem..... (answered by robertb)

Can some please help me solve for x? ln (4x � 8) � ln (x-1) = ln... (answered by josmiceli)