Question

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

Answer 1

x=3

Explanation:

Answer 2

`x=3`

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{(225)/(25) }`

`\boxed{x=3}`