Question

100^x+1=25^x+1

Solve for x
ALSO: remember that the x+1 is also part of the exponent.
Thank you so much!!! :))

Answer 1

There are these things called parentheses that let you avoid awkward notes like "remember that the x+1 is also part of the exponent." But we appreciate the note.

`100^(x+1)=25^(x+1)`

Taking logarithms

`(x+1) \log 100 = (x+1) \log 25`

`(x+1) \log 100 - (x+1) \log 25 = 0`

`(x+1) (\log 100 - \log 25) = 0`

We don't need a calculator or anything; all we need to know is that difference of logs isn't zero.

`x+1=0`

`x=-1`