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.
[tex]100^{x+1}=25^{x+1}[/tex]
Taking logarithms
[tex](x+1) \log 100 = (x+1) \log 25[/tex]
[tex](x+1) \log 100 - (x+1) \log 25 = 0[/tex]
[tex](x+1) (\log 100 - \log 25) = 0[/tex]
We don't need a calculator or anything; all we need to know is that difference of logs isn't zero.
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
