Question

Can you please solve this equation and show the work? 25^1-3x = 125^x-1

Answer 1

\[25^{1-3x} = 125^{x-1}\] is the right equation...

Answer 2

@Zale101 @Data_LG2

Answer 3

HI sorry for the late response..

first thing you have to do is to make the base of terms equal
the common base for 25 and 125 would be 5
so you'll have:
\(\sf 25^{1-3x} = 125^{x-1}\\ 5^{2(1-3x)}=5^{3(x-1)}\)

since both side have the same base already, you can easily solve x in the exponents algebraically:

\(\sf 2(1-3x)=3(x-1)\)
can you do it from here?

Answer 4

X is then equal to 5/9 right?

Answer 5

\(\sf 2(1-3x)=3(x-1)\\2-6x=3x-3\\3x+6x=2+3\\9x=5\\x=5/9\)

yes, looks like you're right :)

Answer 6

Thanks!