Question

Find x: 25(15^x-1) = (3^x-1)

Answer 1

\[25(15^{x-1}) = 3^{x-1}\]

Answer 2

Could someone explain what I should do, step by step?

Answer 3

x=-1

Answer 4

Yes, I know that the answer is x = -1. But, how?

Answer 5

is it correct..?

Answer 6

Yes! :)

Answer 7

first consider x-1=y

Answer 8

then it becomes 25(15^y) = (3^y)

Answer 9

Yes...

Answer 10

15^y=(3^y)(5^y)

Answer 11

cancelling 3^y on both sides...

Answer 12

Thanks!!!

Answer 13

we find 25 (5^y)=1

Answer 14

thus y=-2=x-1

Answer 15

x=-1

Answer 16

hence proved... :)