Question

5^-x=1/25

Answer 1

\[5^{-x} = \frac{1}{25}\]A useful principle of exponents to be remembered is:
\[u^{-n} = \frac{1}{u^n}\]How could we rewrite the left side of the equation using that?

Answer 2

\[5^{-x} = \frac{ 1 }{ 25 }\]
So you can write it like that, assuming that x is positive: \[5^{x} = 25\]
Then: \[x = \frac{ \ln(25) }{ \ln(5) }\]
Which equals to : \[x = 2\]

Answer 3

well, we don't have to assume anything:\[5^{-x} = \frac{1}{5^x}\]

If \[\frac{1}{5^x} = \frac{1}{25}\]then for that to be true, we can cross-multiply to get \[25*1 = 5^x*1\]\[25=5^x\]\(25>5\) so \(x>0\) and it ought to be obvious that \(x=2\) without dusting off the log tables :-)