a) \(\left(2x+\frac{3}{5}\right)^2-\frac{9}{25}=0\)

                 \(\left(2x+\frac{3}{5}\right)^2=\frac{9}{25}\)

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

           \(=>2x+\frac{3}{5}=\frac{3}{5}\)

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

                                    \(2x=0\)

                                      \(x=0:2\)

                                      \(x=0\)

b) \(\left(3x-1\right).\left(-\frac{1}{2x}+5\right)=0\)

=> \(\left(3x-1\right)=0\)hoặc \(\left(-\frac{1}{2x}+5\right)=0\)hoặc \(\left(3x-1\right)\)và\(\left(-\frac{1}{2x}+5\right)\)cùng bằng 0.

\(\orbr{\begin{cases}3x-1=0\\-\frac{1}{2x}+5=0\end{cases}}=>\orbr{\begin{cases}3x=1\\-\frac{1}{2x}=-5\end{cases}}=>\orbr{\begin{cases}x\in\varnothing\\2x=\frac{1}{5}\end{cases}}=>x=\frac{1}{5}:2=>x=\frac{1}{10}\)

a) \(3^{x-1}+3x+3^{x+1}=1053\)

\(=3^x:3+3^x+3^x.3=1053\)

\(=3^x.\dfrac{1}{3}+1+3=1053\)

\(=3^x.\dfrac{13}{5}=1053\)

\(=3^x=243\)

\(\Rightarrow x=5\)

Vậy \(x=5\)

a, 5^x . (5^3)^2=625

5^x . 5^6=5^4

5^x=5^4:5^6

5^x=5^-2

=> x=-2

b)(5.x+1)²=\(\frac{36}{49}\)

\(\Rightarrow\)5.x+1=\(\sqrt{\frac{36}{49}}\)=\(\frac{6}{7}\)

\(\Rightarrow\)5.x=\(\frac{6}{7}\)-1=\(\frac{-1}{7}\)

\(\Rightarrow\)x=\(\frac{-1}{7}\):5=\(\frac{-1}{35}\)

Vậy x=\(\frac{-1}{35}\)

Chúc bạn học tốt!

a: =>2x+5=4

=>2x=-1

hay x=-1/2

b: \(\Leftrightarrow\left(3x-4\right)^2\cdot\left[\left(3x-4\right)^2-1\right]=0\)

=>(3x-4)(3x-5)(3x-3)=0

hay \(x\in\left\{1;\dfrac{4}{3};\dfrac{5}{3}\right\}\)

c: \(\Leftrightarrow3^{x+1}=3^{2x}\)

=>2x=x+1

=>x=1

d: \(\Leftrightarrow2^{2x+3}=2^{2x-10}\)

=>2x+3=2x-10

=>0x=-13(vô lý)

a: \(5^{x}\cdot\left(5^3\right)^2=625\)

=>\(5^{x}=\frac{5^4}{5^6}=5^{-2}\)

=>x=-2

b: \(\left(\frac{12}{15}\right)^{x}=\left(\frac53\right)^{-5}-\left(-\frac35\right)^4\)

=>\(\left(\frac45\right)^{x}=\left(\frac35\right)^5-\left(\frac35\right)^4=\left(\frac35\right)^4\cdot\left(\frac35-1\right)=\left(\frac35\right)^4\cdot\frac{-2}{5}=\frac{-2\cdot3^4}{5^5}\)

=>\(x=\log_{0,8}\left(-2\cdot\frac{3^4}{5^5}\right)\)

c: \(\left(-\frac34\right)^{3x-1}=\frac{256}{81}\)

=>\(\left(-\frac34\right)^{3x-1}=\left(-\frac34\right)^{-4}\)

=>3x-1=-4

=>3x=-3

=>x=-1

d: \(172x^2-7^9:98^3=2^{-3}\)

=>\(172x^2=\frac18+\frac{7^9}{7^6\cdot2^3}=\frac18+\frac{7^3}{2^3}=\frac{1+343}{8}=\frac{344}{8}\)

=>\(x^2=\frac{344}{8}:172=\frac{344}{8\cdot172}=\frac28=\frac14\)

=>\(\left[\begin{array}{l}x=\frac12\\ x=-\frac12\end{array}\right.\)

Bài 1: 

a: \(\Leftrightarrow3^x\cdot10=810\)

\(\Leftrightarrow3^x=81\)

hay x=4

c: \(\Leftrightarrow5^x\cdot5+5^x\cdot\dfrac{1}{25}=126\)

\(\Leftrightarrow5^x\cdot\dfrac{126}{25}=126\)

\(\Leftrightarrow5^x=25\)

hay x=2

Bài 2: 

a: \(27^{11}=3^{33}\)

\(81^8=3^{32}\)

mà 33>32

nên \(27^{11}>81^8\)

c: \(625^5=\left(5^4\right)^5=5^{20}\)

\(125^7=\left(5^3\right)^7=5^{21}\)

mà 20<21

nên \(625^5< 125^7\)

(-3/4)63x-1=(3/4)^3

3x-1=3+1

3x=3=1

x=4;3

x=4/3

Vậy x=4/3

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