i am having trouble with logs...log5^25x - Log5^x=2...where do i start?

Answer 1

Use the log rules. log x^a = a log x. log a - log b = log (a/b). So

log 5^25x - log 5^x = 2
log ( 5^25x / 5^x) = 2
log 5^24x = 2
24x • log 5 = 2
x = 2 / (24 log 5)
x = 0.11922

Answer 2

log[a^(b)] = (b)log[a]
Therefore
log[5^(25x)] = (25x)log[5]
and
log[5^(x)] = (x)log[5]

Substituting these in, you get
(25x)log5 - (x)log5 = 2
Simplify to
(24x)log5 = 2

Then solve for x
x = 1/(24log5) ~ 0.1192