This is about Logarithms. How do I do this problem? ln(x+6)-ln5=ln(2x-7) I am clueless.?

Question

I have tried several different ways and it just doesnt seem right to me. Please help!!

Answer 1

ln(x+6)-ln5=ln(x+6)/5 difference rule
ln(x+6)/5=ln(2x-7) given
since the logs are equal removing the log sign
(x+6)/5=2x-7
multiplying by 5
x=6=5(2x-7)
x+6=10x-35
adding -6
x=10x-41
adding-x
0=9x-41
adding 41
9x=41
dividing by 9
x=41/9

Answer 2

What you are missing is a very basic understanding of
logaritmic operations. Here are the fundamentals.

Rule 1
ln(a) + ln(b) = ln(ab)
Rule 2
ln(a) - ln(b) = ln(a/b)
Rule 3
ln(a^b) = (b)ln(a)

Your problem uses the 2nd rule.
ln(x+6)-ln5 = ln{(x+6)/5}. Now we can rewrite the equation
ln{(x+6)/5} = ln(2x-7) and take the anti ln of both sides giving
(x+6)/5 = 2x-7
x+6 = 10x-35
9x=41
x=41/9

Answer 3

ln(x+5)- ln5 = ln(2x-7)
=> ln((x+5)/5) = ln (2x-7)
by taking antilogarithem
(x+5)/5 = 2x - 7
=> x+5=10x - 35
=> x-10x = -35-5
=> -9x = -40
=> x = 40/9

Answer 4

first, use ln(a) - ln(b) = ln(a/b):
ln(x + 6) - ln5 = ln(2x - 7)
ln((x + 6)/5) = ln(2x - 7)
Now you can use [if a = b then ln(a) = ln(b)]
(x + 6)/5 = 2x - 7
Multiply through by 5:
x + 6 = 10x - 35
9x = 41
x = 41/9

Answer 5

ln(x+6)-ln5=ln(2x-7)
ln((x+6)/5)=ln(2x-7)
(x+6)/5=2x-7
x+6=10x-35
41=9x
x=4 5/9