Question

Simplify the expression: ln10-ln(x+6)=5 I know that the answer is: {10-6e^5/e^5} But I don't know how to work out the problem.

Answer 1

Log's properties and exponential function. What happens when you apply a function and its inverse?

Answer 2

I'm not sure exactly.

Answer 3

Just use the basic rule for the logarithm:
ln(a) - ln(b) = ln(a / b)

ln10 - ln(x+6) = 5
ln(10 / (x+6)) = 5

Then use the inverse function to logarithm - the exponential function:
ln(10 / (x+6)) = 5
exp( ln(10 / (x+6)) ) = exp(5)
10 / (x+6) = exp(5)
10 / exp(5) = x + 6
(10 - 6*exp(5)) / exp(5) = x

Answer 4

Oh and by exp(5) I mean e^5 of course. It's the same thing.

Answer 5

Thank you :)