Question 412674
{{{ln(x+3)^5<5}}}
First we can use a property of logarithms, {{{log(a, (p^q)) = q*log(a, (p))}}}, to move the exponent of the argument out in front:
{{{5*ln(x+3)<5}}}
Next we can divide both sides by 5:
{{{ln(x+3)<1}}}
Since ln(e) = 1
x+3 < e
Subtracting 3 from each side we get:
x < e-3<br>
We also have to consider the fact that arguments of logarithms must always be positive. For this reason
x+3 > 0
Subtracting 3 from eqach side we get:
x > -3<br>
Putting these together we have
x < e-3 and x > -3
This is the solution to your inequality.