How would I solve: ln(9 x + 6) - ln(5 x ) = 7

Question

ln(9 x + 6) - ln(5 x ) = 7

 

I'm not sure how to go about this, any help would be appreciated!

Answer 1

Using the logarithmic property that Joshua mentioned here, we would end up with

 

ln[(9x + 6) / 5x] = 7

 

 

The solution to a natural log is the exponent of the base number e.  e is approximately 2.7.  If it were log, then the base number would have been 10.  So the equation we get from this concept is

 

e⁷ = (9x + 6) / 5x

 

 

Now just solve for x from the equation.  You may leave the solution in terms of e.

Answer 2

Properties of logarithm. When adding two or more logarithms, you can turn it into one logarithm while their contents will be multiplied. Ex. ln(x)+ln(y) = ln(xy). If it's subtraction then you'll divide it. Ex. ln(x)-ln(y)= ln(x/y)