a) (2x - 3)² = 16

=> (2x - 3)² = 4²

=> 2x - 3 = \(\pm\) 4

TH1: 2x - 3 = 4

=> 2x = 4 + 3

=> 2x = 7

=> x = \(\dfrac{7}{2}\)

TH2: 2x - 3 = -4

=> 2x = -4 + 3

=> 2x = -1

=> x = \(\dfrac{-1}{2}\)

Vậy x= \(\dfrac{7}{2}\) ; x = \(\dfrac{-1}{2}\)

b) (7x + 2)^-1 =3^-2

=> \(\dfrac{1}{7x+2}\) = \(\dfrac{1}{9}\)

=> 7x + 2 = 9

=> 7x = 9 - 2

=> 7x = 7

=> x = 1

Tính (15^5:5^5).(3^5:6^5)

Trả lời : 

A. 243/32

đáp án A

1. 3 ^{x + 1} = 9 ^x

    3 ^{x + 1} = 3 ^{2 x}

=> x + 1 = 2 x

    x - 2x = -1

   -x       = -1

=> x = 1

2 . 2 ^{3x + 2} = 4 ^{x + 5}

     2 ^{3x + 2} = 2 ^{2. ( x + 5 )}

=> 3x + 2 = 2 ( x + 5 )

     3x + 2 = 2x + 10

     3x -2x = 10 - 2

     x         = 8

3 . 3 ^{2 x - 1} = 243

=> 3 ^{2 x - 1} = 3 ⁵

=> 2 x - 1 = 5

     2 x      = 6

       x       = 3

\(5^{x+2}+5^{x+3}=750\)

\(5^x.5^2+5^x.5^3=750\)

\(5^x.25+5^x\cdot125=750\)

\(5^x.\left(25+125\right)=750\)

\(5^x.150=750\)

\(5^x=750:150\)

\(5^x=5\)

\(5^x=5^1\)

\(\Rightarrow x=1\)

a)(2x-3)²=16

=>2x-3=4 hoặc 2x-3=-4

<=>2x=7 hoặc 2x=-1

<=>x=7/2 hoặc x=-1/2

b)(3x-2)⁵=243=3⁵

=>3x-2=3

=>3x=5

=>x=5/3

c)(7x+2)^-1=5²

<=>\(\frac{1}{7x+2}=25\)

<=>25(7x+2)=1

<=>175x+50=1

<=>175x=-49

<=>x=-49:175

<=>x=-7/25

d)(x-3/4)⁴=81=3⁴=(-3)⁴

=>x-3/4=3 hoặc x-3/4=-3

<=>x=3+3/4 hoặc x=-3+3/4

<=>x=15/4 hoặc x=-9/4

tìm x,biết:(7x+2)^-1=3^-2

a) \(\left(x-1\right)^5=-243\)

\(\Rightarrow\left(x-1\right)^5=\left(-3\right)^5\)

\(\Rightarrow x-1=-3\)

\(\Rightarrow x=\left(-3\right)+1\)

\(\Rightarrow x=-2\)

Vậy \(x=-2.\)

b) \(\left|5x-3\right|-2x=14\)

\(\Rightarrow\left|5x-3\right|=14+2x.\)

\(\Rightarrow\left[{}\begin{matrix}5x-3=14+2x\\5x-3=-14-2x\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}5x-2x=14+3\\5x+2x=-14+3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}3x=17\\7x=-11\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=17:3\\x=\left(-11\right):7\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{17}{3}\\x=-\frac{11}{7}\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{17}{3};-\frac{11}{7}\right\}.\)

Chúc bạn học tốt!

Mình chỉ biết là 3⁵=243

k nhé

Chúc bạn học giỏi

\(3^{2x-1}=243\)

\(\Rightarrow3^{2x-1}=3^5\)

\(\Rightarrow2x-1=5\)

\(\Rightarrow2x=5+1\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=6:2\)

\(\Rightarrow x=3\)

a) \(\left(-\frac{1}{2}\right)^n=\frac{1}{64}\)

\(\left(-\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^6\)

\(\left(-\frac{1}{2}\right)^n=\left(-\frac{1}{2}\right)^6\)

\(\Rightarrow n=6\)

b) \(\frac{2^n}{32}=2\)

\(2^n=2.32\)

\(2^n=64\)

\(2^n=2^6\)

\(\Rightarrow n=6\)

c) \(\left(-3\right)^3.\left(-3\right)^n=-243\)

\(\left(-3\right)^{3+n}=\left(-3\right)^5\)

\(\Rightarrow3+n=5\)

               \(n=5-3\)

               \(n=2\)

a, ( - 1/2)ⁿ  = (1/2)⁶

       n = 6

2ⁿ = 2 . 32 = 64

2ⁿ = 2⁶

n = 6

(-3)^{3 .}  (-3)ⁿ = (-3)⁵

(-3)ⁿ = (-3)²

n = 2

1)(x-3)²=0

=>x-3=0

x=0+3

x=3

2)(2x+1)²=4=2²

=>2x+1=2

2x=2-1

2x=1

x=1/2

3)(2x-3)³=8=2³

=>2x-3=2

2x=2+3

2x=5

x=5/2

4)(x+1/2)⁴=1/16=(1/4)⁴

=>x+1/2=1/4

x=1/4-1/2=1/4-2/4

x=-1/4

5)9,27<=3^x<=243

3²<=3^x<=3⁵ (vì x thuộc Z nên làm tròn số 9,27)

=>x thuộc{3;4}

\(x^2=\frac{1}{16}=\left(\frac{1}{4}\right)^1=\left(-\frac{1}{4}\right)^2\)

Vậy có 2 ngiệm x

TH1: \(x=\frac{1}{4}\)

TH2: \(x=-\frac{1}{4}\)

x²=1/16
=>x=1/4; x=-1/4
x⁵=(2/3)⁵
=>x=2/3
x⁴=(3/2)⁴
=>x=3/2; x=-3/2