Logarithm Inequality: Solving 3(1-3^x) < 5^x(1-3^x)

[scientifico]

Homework Statement

3 - 3^(x+1) < 5^x - 15^x

3(1-3^x) < 5^x(1-3^x)

Do I have to impose 1-3^x > 0 ?

It results x<0 and x>log(5,3) but book has written 0 < x < log(5,3) where did I wrong ?

 

[tiny-tim]

hi scientifico!

(try using the X² button just above the Reply box )

Do I have to impose 1-3^x > 0 ?

no, you can't do that, you don't know that it's true!

either you must deal separately with 1-3^x > 0 and 1-3^x < 0.

or just write (1-3^x)(3-5^x) < 0