5^-x=1/25

Question

5^-x=1/25

whpalmer4 · Answer

$$5^{-x} = \frac{1}{25}$$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?

anonymous · Answer

$$5^{-x} = \frac{ 1 }{ 25 }$$
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 : $$x = 2$$

whpalmer4 · Answer

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 :-)