Bài 6 :

a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)

b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)

c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)

d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)

Bài 7 :

a) \(3^x+3^{x+2}=9^{17}+27^{12}\)

\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)

\(\Rightarrow10.3^x=3^{34}+3^{36}\)

\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)

\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)

b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)

\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)

\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)

c) Bài C bạn xem lại đề

d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)

\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)

\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)

\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)

\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)

\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)

a) Ta có: \(\left(\frac{1}{2}\right)^m=\frac{1}{32}\)

Mà \(\frac{1}{32}=\left(\frac{1}{2}\right)^5\)

\(\Rightarrow\left(\frac{1}{2}\right)^m=\left(\frac{1}{2}\right)^5\Rightarrow m=5\)

b)Ta có:  \(\frac{343}{125}=\left(\frac{7}{5}\right)^3\)

Mà \(\left(\frac{7}{5}\right)^3=\left(\frac{7}{5}\right)^n\Rightarrow n=3\)

\(a)\) \(\left(\frac{1}{2}\right)^m=\frac{1}{32}\)

\(\Leftrightarrow\)\(\left(\frac{1}{2}\right)^m=\frac{1^5}{2^5}\)

\(\Leftrightarrow\)\(\left(\frac{1}{2}\right)^m=\left(\frac{1}{2}\right)^5\)

\(\Leftrightarrow\)\(m=5\)

Vậy \(m=5\)

\(b)\) \(\frac{343}{125}=\left(\frac{7}{5}\right)^n\)

\(\Leftrightarrow\)\(\frac{7^3}{5^3}=\left(\frac{7}{5}\right)^n\)

\(\Leftrightarrow\)\(\left(\frac{7}{5}\right)^3=\left(\frac{7}{5}\right)^n\)

\(\Leftrightarrow\)\(n=3\)

Vậy \(n=3\)

Chúc bạn học tốt ~ 

Bạn nên viết đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để mọi người hiểu đề của bạn hơn.

\(\left(\dfrac{3}{5}\right)^{10}\cdot\left(\dfrac{5}{3}\right)^{10}-\dfrac{13^4}{39^4}+2014^0\)

=1-(1/3)^4+1

=4/3-1/81

=107/81

(1/2)^m = 1/32

mà 1/32 = (1/2)^5 nên m = 5

343/125= (7/5)^n

mà 343/125 = (7/5)^3 nên n=3

Ta có : \(\frac{2^7.3^4}{3^3.2^5}=\frac{2^2.3}{1.1}=4.3=12\)

k cho mk nha!

Ta lập biểu thức:

\(\frac{\left(2^7.3^4\right)}{3^3.2^5}=\frac{128.81}{27.32}=\frac{10368}{864}=12\)

Vì khi ta lập biểu thức ra và tính nó sẽ được vậy chứ khong có lí do nha bạn ~~

còn 3 câu sau thì sao vậy bn