Question

Tìm n ∈ N biết

a)\(\dfrac{625}{5^n}=5\)

b)\(\dfrac{\left(-2\right)^n}{16}=-32\)

Answer 1

a)\(\dfrac{625}{5^n}=5\)\(\Rightarrow\)\(\dfrac{5^4}{5^n}=5\)\(\Rightarrow\)\(5^n=5^5:5^4=5^1\Rightarrow n=1\)

b)\(\dfrac{\left(-2\right)^n}{16}=-32\Rightarrow\)\(\left(-2\right)^n=-32.16=\left(-1\right).2^5.2^4=\left(-1\right).2^9=\left(-2\right)^9\)

.............................\(\Rightarrow n=9\)

Answer 2

a. \(\dfrac{625}{5^n}=5\Rightarrow5^n=\dfrac{625}{5}=125\Rightarrow5^n=5^3\Rightarrow n=3\left(TMĐK\right)\)

Vậy n=3

b. \(\dfrac{\left(-2\right)^n}{16}=-32\Rightarrow\left(-2\right)^n=-32\cdot16=-512\Rightarrow\left(-2\right)^n=\left(-2\right)^9\Rightarrow n=9\left(TMĐK\right)\)

Vậy n=9