\(a.\)

\(x:\left(\frac{3}{4}\right)^3=\left(\frac{3}{4}\right)^2\)

\(\Rightarrow x=\left(\frac{3}{4}\right)^2.\left(\frac{3}{4}\right)^3\)

\(\Rightarrow x=\left(\frac{3}{4}\right)^5\)

Vậy :   \(x=\left(\frac{3}{4}\right)^5\)

\(b.\)

\(\left(\frac{2}{5}\right)^5.x=\left(\frac{2}{5}\right)^8\)

\(\Rightarrow x=\left(\frac{2}{5}\right)^8:\left(\frac{2}{5}\right)^5\)

\(\Rightarrow x=\left(\frac{2}{5}\right)^3\)

Vậy :   \(x=\left(\frac{2}{5}\right)^3\)

a/ x : ( 3/4 )³= ( 3/4 )²

=> x = ( 3/4 )². ( 3/4 )³

=> x = ( 3/4 )⁵

vậy x = ( 3/4 )⁵

b/ ( 2/5 )⁵. x = ( 2/5 )⁸

=> x = ( 2/5 )⁸: ( 2/5 )⁵

=> x = ( 2/5 )³

vậy x = ( 2/5 )³ 

Giải:

a) \(\dfrac{1}{3}x+\dfrac{1}{5}-\dfrac{1}{2}x=1\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{1}{5}-\dfrac{1}{6}x=\dfrac{5}{4}\)

\(\Leftrightarrow\dfrac{1}{6}x=\dfrac{-21}{20}\)

\(\Leftrightarrow x=\dfrac{-63}{10}\)

Vậy ...

b) \(\dfrac{3}{2}\left(x+\dfrac{1}{2}\right)-\dfrac{1}{8}x=\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{3}{2}x+\dfrac{3}{4}-\dfrac{1}{8}x=\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{11}{8}x=\dfrac{-1}{2}\)

\(\Leftrightarrow x=\dfrac{-4}{11}\)

Vậy ...

Các câu sau làm tương tự câu b)

a,\(x-\dfrac{3}{5}=\dfrac{3}{5}\)

\(x=\dfrac{3}{5}+\dfrac{3}{5}\)

\(x=\dfrac{6}{5}\)

b,\(\left|x\right|-\dfrac{4}{5}=\dfrac{2}{5}\)

\(\left|x\right|=\dfrac{2}{5}+\dfrac{4}{5}\)

\(\left|x\right|=\dfrac{6}{5}\)

\(\Rightarrow x=\pm\dfrac{6}{5}\)

c,\(\dfrac{x}{-5}=\dfrac{24}{15}\)

\(x=\dfrac{-5.24}{15}\)

\(x=\dfrac{-24}{5}\)

d,Áp dụng tc dãy TSBN, ta có:

\(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{x-y}{4-5}=\dfrac{21}{-1}=-21\)

+\(\dfrac{x}{4}=-21\Rightarrow x=-21.4=-84\)

+\(\dfrac{y}{5}=-21\Rightarrow y=-21.5=-105\)

Vậy x=-84 ; y=-105

a/ \(x-\dfrac{3}{5}=\dfrac{3}{5}\)

\(\Leftrightarrow x=\dfrac{3}{5}+\dfrac{3}{5}\)

\(\Leftrightarrow x=\dfrac{6}{5}\)

Vậy...

b/ \(\left|x\right|-\dfrac{4}{5}=\dfrac{2}{5}\)

\(\Leftrightarrow\left|x\right|=\dfrac{2}{5}+\dfrac{4}{5}\)

\(\Leftrightarrow\left|x\right|=\dfrac{6}{5}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{6}{5}\\x=-\dfrac{6}{5}\end{matrix}\right.\)

Vậy...

c/ \(\dfrac{x}{-5}=\dfrac{24}{15}\)

\(\Leftrightarrow15x=-120\)

\(\Leftrightarrow x=-8\)

Vậy...

c/ Theo t/c dãy tỉ số bằng nhau ta có :

\(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{x-y}{4-5}=\dfrac{21}{-1}=-21\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{4}=-21\\\dfrac{y}{5}=-21\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-84\\y=-105\end{matrix}\right.\)

Vậy..

\(\dfrac{5}{6}x-\dfrac{3}{4}=\dfrac{-1}{4}+\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{5}{6}x=\dfrac{7}{6}\)

\(\Rightarrow x=\dfrac{7}{5}\)

b) \(-1\dfrac{1}{2}-\dfrac{2}{3}x=\dfrac{5}{6}-\left(\dfrac{-2}{5}\right)\)

\(\Leftrightarrow\dfrac{2}{3}x=-\dfrac{41}{15}\)

\(\Rightarrow x=-\dfrac{41}{10}\)

c) \(\left(\dfrac{4}{5}:x+1,5\right):\dfrac{2}{3}=-1,5\)

\(\Leftrightarrow\dfrac{8+15x}{10x}.\dfrac{3}{2}=\dfrac{-3}{2}\)

\(\Leftrightarrow\dfrac{24+45x}{20x}=\dfrac{-3}{2}\)

\(\Leftrightarrow-60x=48+90x\)

\(\Rightarrow x=-0,32\)

d) \(\dfrac{4}{3}x-\dfrac{2}{3}=\dfrac{1}{4}-x\)

\(\Leftrightarrow\dfrac{4x-2}{3}=\dfrac{1-4x}{4}\)

\(\Rightarrow16x-8=3-12x\)

\(\Rightarrow x=\dfrac{11}{28}\)

a) \(\frac{-2^2}{3}.x=\frac{-2^5}{3}\)

                 \(x=\frac{-2^5}{3}:\frac{-2^2}{3}\)

                 \(x=\frac{-2^5}{3}.\frac{-3}{2^2}\)

                 \(x=\frac{2^3}{1}\)

                 \(x=2^3\)

                 \(x=8\)

Vậy x = 8

b)\(\frac{-1^3}{3}.x=\frac{1}{81}\)

                \(x=\frac{1}{81}:\frac{-1^3}{3}\)

                \(x=\frac{1}{81}.\frac{-3}{1^3}\)

                \(x=\frac{1}{3^4}.\frac{-3}{1^3}\)

                \(x=\frac{1}{3^3}.\frac{-1}{1^2}\)

                \(x=\frac{-1}{3^3}\)

                \(x=\frac{-1}{27}\)

Vậy \(x=\frac{-1}{27}\)

a)4^x+4^x+3=4160

=>4^x(1+4³)=4160

=>4^x*65=4160

=>4^x=64

=>4^x=4³

=>x=3

b)Bạn xem lại đề vì số hơi lẻ