ln of a number?

Question

ln 1.5 / x = 0.308

how do i get rid of the ln so that i can solve for x?

Answer 1

Raise the number e to the power of each side of the equation.

ln (1.5/x) = 0.308
e^(ln (1.5/x)) = e^0.308
1.5/x = e^0.308
x = 1.5 / e^0.308

I assumed that 1.5/x was the argument of the ln function. You may have meant that (ln 1.5) was to be divided by x, but in that case you wouldn't need to eliminate the ln function; you'd just evaluate it after performing the simple algebra to isolate x.

In any event, e^(ln(x)) = x for any value or expression for x, so e^(ln (1.5/x)) = 1.5/x, so that's how you get rid of ln.

Answer 2

ln 1.5 / x = 0.308

Multiply both sides by (x/.308):

(ln 1.5) / .308 = x = .405465/.308 = 1.316445

Answer 3

I assume you mean ln(1.5/x) = 0.308 since there's not much to discuss about the simpler equation ln(1.5)/x = 0.308...

Well, take the exponential of both sides ("exp" is the inverse of "ln").

1.5 / x = exp(0.308)

Then, it's a simple matter to solve for x, namely:

x = 1.5 / exp(0.308)

Equivalenty: x = 1.5 exp(-0.308) =1.102372977...

Answer 4

Assume question is:-
ln (1.5 / x) = 0.308
1.5 / x = e^(0.308)
1.5 / x = 1.36
1.5 = 1.36 x
x = 1.5 / 1.36
x = 1.1

Answer 5

if lnx=y
simply x=e^y
hence
ln 1.5/x =.308
1.5/x=e^0.308
hence x=1.5(e^-.308)
e value can be approximated to 2.7

Answer 6

ln(1.5/x)=0.308
1.5/x=1.3607
x=1.5/1.3607=1.1024 answer