Use the definition of the logarithm function:
Where the base is
Which is to say
for the exact answer. Use your calculator for a decimal approximation to the precision of your choice.
John
My calculator said it, I believe it, that settles it
2·ln(x-6) = -4
Divide both sides by 2
ln(x-6) = -2
To finish this problem, you must know enough about logarithms
to know how to convert a logarithm equation into an exponential
equation. That is, you have to know that any logarithm equation
of the form ln(A) = B is equivalent to the exponential equation
A = eB.
So ln(x-6) = -2 converts to the exponential equation
x-6 = e-2
Then solve for x
x = 6+e-2
That's as far as you can take it without going into decimals.
Using a calculator you can get the decimal approximation:
x = 6.135335283
Edwin