Question

5^(2x-3)=25^(3x+1) solve for x

Answer 1

first you must know that ln(a^x) = xln(a)

so if we introduce the ln here for both sides
ln{5^(2x-3)}=ln{25^(3x+1)}
(2x-3)ln5 = (3x+1)ln25
(2x-3)ln5 = (3x+1)ln(5^2)
(2x-3)ln5 = 2(3x+1)ln5 divide by ln5
2x-3 = 2(3x+1)
2x-3 = 6x +2
-4x = 5
x = -5/4

Answer 2

Wow, thanks, over teacher didn't show us this rule so I didn't know how to solve.

Answer 3

what happens when I have ln16 and ln8? how do i cancel those?

Answer 4

ln16 = ln(2^4) = 4ln2
ln8 = ln(2^3) = 3ln2

Answer 5

ohh I see. Thanks!

Answer 6

any time :)