Question

What is the true solution to 2 in e^in5x =2 in 15

Answer 1

Answer:

$x=3$

Step-by-step explanation:

Assuming your original equation is

$2ln(e^{ln(5x)})=2ln(15)$

by the logarithm property $a*log(b)=log(b^a)$ this equation becomes

$ln(e^{2ln(5x)})=ln(225)$

This means

$e^{2ln(5x)}=225$

Take the natural logarithm of both sides and get:

$2ln(5x)=ln(225)$

By the same lograthim property $a*log(b)=log(b^a)$, the left side is modified:

$ln(25x^2)=ln(225)$

which gives

$25x^2=225$

or

$x=\sqrt{\frac{225}{25} }$

$\boxed{x=3}$

Answer 2

Answer:

x=3

Step-by-step explanation: