Answer:
[tex]x=3[/tex]
Step-by-step explanation:
Assuming your original equation is
[tex]2ln(e^{ln(5x)})=2ln(15)\\[/tex]
by the logarithm property [tex]a*log(b)=log(b^a)[/tex] this equation becomes
[tex]ln(e^{2ln(5x)})=ln(225)[/tex]
This means
[tex]e^{2ln(5x)}=225[/tex]
Take the natural logarithm of both sides and get:
[tex]2ln(5x)=ln(225)[/tex]
By the same lograthim property [tex]a*log(b)=log(b^a)[/tex], the left side is modified:
[tex]ln(25x^2)=ln(225)[/tex]
which gives
[tex]25x^2=225[/tex]
or
[tex]x=\sqrt{\frac{225}{25} }[/tex]
[tex]\boxed{x=3}[/tex]
