\(\left(x-\frac{2}{3}\right)^3=-0,421875\)

\(x-\frac{2}{3}=\sqrt[3]{-0,421875}\)

tới đây chắc tự làm đc

a) \(2^{4x+1}-8^{x+2}=0\)\(\Leftrightarrow2^{4x+1}-2^{3\left(x+2\right)}=0\)

\(\Leftrightarrow2^{4x+1}-2^{3x+6}=0\)\(\Leftrightarrow2^{4x+1}=2^{3x+6}\)

\(\Leftrightarrow4x+1=3x+6\)\(\Leftrightarrow4x-3x=6-1\)\(\Leftrightarrow x=5\)

Vậy \(x=5\)

b) \(3^2.9^{2x}=27^{x+3}\)\(\Leftrightarrow3^2.3^{2.2x}=3^{3\left(x+3\right)}\)\(\Leftrightarrow3^2.3^{4x}=3^{3x+9}\)

\(\Leftrightarrow3^{2+4x}=3^{3x+9}\)\(\Leftrightarrow2+4x=3x+9\)\(\Leftrightarrow4x-3x=9-2\)\(\Leftrightarrow x=7\)

Vậy \(x=7\)

c) \(8^{2x}.64^2=16^{x+4}\)\(\Leftrightarrow2^{3.2x}.2^{6.2}=2^{4\left(x+4\right)}\)\(\Leftrightarrow2^{6x}.2^{12}=2^{4\left(x+4\right)}\)

\(\Leftrightarrow2^{6x+12}=2^{4x+16}\)\(\Leftrightarrow6x+12=4x+16\)\(\Leftrightarrow6x-4x=16-12\)

\(\Leftrightarrow2x=4\)\(\Leftrightarrow x=2\)

Vậy \(x=2\)

\(3^x.3^3=81\)

<=> \(3^x=3\)

<=> \(x=1\)

1.

a) a=5 vì 5² = 25

b) a=3 vì 3³ = 27

2.

a)x=2 vì 5² = 25

b ) x= 4 vì 4³ = 64

c ) x=1 vì 2¹ . 2 =4

chúc bn hok giỏi

bài 1

\(a=5\)

\(b=3\)

a) \(3^{x-2}=27\cdot9\)

\(3^{x-2}=3^3\cdot3^2=3^5\)

\(\Rightarrow\)\(x-2=5\Rightarrow x=7\)

b) \(2^{x+1}+2^{x+3}=80\)

\(\Rightarrow2^{x+1}\left(1+2^2\right)=80\)

\(\Rightarrow2^{x+1}\cdot5=80\)

\(\Rightarrow2^{x+1}=16=2^4\)

\(\Rightarrow x+1=4\Rightarrow x=3\)

c) \(2^{2x-3}=16\cdot8\)

\(2^{2x-3}=2^4\cdot2^3=2^7\)

\(\Rightarrow2x-3=7\)

\(\Rightarrow2x=4\Rightarrow x=2\)

d) \(2^{x-2}\cdot2^x=64\)

\(\Rightarrow2^{x-2+x}=64=2^6\)

\(\Rightarrow x-2+x=6\)

\(\Rightarrow2x-2=6\)

\(\Rightarrow2x=8\Rightarrow x=4\)

Giải:

a) \(3^{x-2}=27.9\)

\(\Leftrightarrow3^{x-2}=3^3.3^2\)

\(\Leftrightarrow3^{x-2}=3^5\)

Vì \(3=3\)

Nên \(x-2=5\)

\(\Leftrightarrow x=5+2\)

\(\Leftrightarrow x=7\)

Vậy x = 7.

b) \(2^{x+1}+2^{x+3}=80\)

\(\Leftrightarrow2^{x+1}\left(1+2^2\right)=80\)

\(\Leftrightarrow2^{x+1}.5=80\)

\(\Leftrightarrow2^{x+1}=\dfrac{80}{5}=16\)

\(\Leftrightarrow2^{x+1}=2^4\)

Vì \(2=2\)

Nên \(x+1=4\)

\(\Leftrightarrow x=4-1\)

\(\Leftrightarrow x=3\)

Vậy x = 3.

c) \(2^{2x-3}=16.8\)

\(\Leftrightarrow2^{2x-3}=2^4.2^3\)

\(\Leftrightarrow2^{2x-3}=2^7\)

Vì \(2=2\)

Nên \(2x-3=7\)

\(\Leftrightarrow2x=7+3=10\)

\(\Leftrightarrow x=\dfrac{10}{2}=5\)

Vậy x = 5.

d) \(2^{x-2}.2^x=64\)

\(2^{2x-2}=2^6\)

Vì \(2=2\)

Nên \(2x-2=6\)

\(\Leftrightarrow2x=6+2=8\)

\(\Leftrightarrow x=\dfrac{8}{2}=4\)

Vậy x = 4.

Chúc bạn học tốt!

a: \(\Leftrightarrow x^3=\dfrac{539}{64}\)

hay \(x=\dfrac{7\sqrt{11}}{4}\)

c: \(\Leftrightarrow2^{2x-1}=2^9\cdot2^2=2^{11}\)

=>2x-1=11

hay x=6

d: \(\Leftrightarrow x^{17}-x=0\)

\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)=0\)

hay \(x\in\left\{0;1;-1\right\}\)

a)\(\left(x-2,5\right)^2=\frac{4}{9}\\ \left(x-\frac{5}{2}\right)^2=\left(\pm\frac{2}{3}\right)^2\\\Leftrightarrow\left\{{}\begin{matrix}x-\frac{5}{2}=\frac{2}{3}\\x-\frac{5}{2}=\frac{-2}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{19}{6}\\x=\frac{11}{6}\end{matrix}\right. \)

vậy....

b)\(\left(2x+\frac{1}{3}\right)^3=\frac{-8}{27}\\ \left(2x+\frac{1}{3}\right)^3=\left(\frac{-2}{3}\right)^3\\ 2x+\frac{1}{3}=\frac{-2}{3}\\ x=\frac{-1}{2}\)

vậy...

2^x=8 hay 2.2.2=8

=>x=3

x^3=64 

=>x =4

D, x = 1

C, x = 6

màu giải như cái lồnn vậy

a) \(-27.43+x=27.57\)\(\Leftrightarrow x=27.57-\left(-27.43\right)\)

\(\Leftrightarrow x=27.57+27.43\)\(\Leftrightarrow x=27.\left(57+43\right)\)

\(\Leftrightarrow x=27.100\)\(\Leftrightarrow x=2700\)

Vậy \(x=2700\)

b) \(3\left(x-2\right)+5\left(3-x\right)=3\)\(\Leftrightarrow3x-6+15-5x=3\)

\(\Leftrightarrow3x-5x=3+6-15\)\(\Leftrightarrow-2x=-6\)\(\Leftrightarrow x=3\)

Vậy \(x=3\)

c) \(3^x=27\)\(\Leftrightarrow3^x=3^3\)\(\Leftrightarrow x=3\)

Vậy \(x=3\)

d) \(2^x+17=-15\)\(\Leftrightarrow2^x=-32\)( vô nghiệm )

Vậy \(x\in\varnothing\)

e) \(\left(x-2\right)^2=9\)\(\Leftrightarrow\orbr{\begin{cases}x-2=-3\\x-2=3\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=5\end{cases}}\)

Vậy \(x=-1\)hoặc \(x=5\)

f) \(\left(x-2\right)^3=27\)\(\Leftrightarrow\left(x-2\right)^3=3^3\)\(\Leftrightarrow x-2=3\)\(\Leftrightarrow x=5\)

Vậy \(x=5\)

g) \(\left(x-2\right)^3=-27\)\(\Leftrightarrow\left(x-2\right)^3=\left(-3\right)^3\)\(\Leftrightarrow x-2=-3\)\(\Leftrightarrow x=-1\)

Vậy \(x=-1\)