a, \(\left(\frac{1}{2}-\frac{1}{3}\right)\cdot6^x+6^{x+2}=6^{10}+6^7\)

\(\Leftrightarrow\frac{1}{6}\cdot6^x+6^x\cdot6^2=6^{10}+6^7\)

\(\Leftrightarrow6^{x-1}\left(1+6^3\right)=6^7\left(6^3+1\right)\)

\(\Leftrightarrow6^{x-1}=6^7\Leftrightarrow x-1=7\)

\(\Leftrightarrow x=8\)

b, \(\left(\frac{1}{2}-\frac{1}{6}\right)\cdot3^{x+4}-4\cdot3^x=3^{16}-4\cdot3^{13}\)

\(\Leftrightarrow\frac{1}{3}\cdot3^{x+4}-4\cdot3^x=3^{13}\left(3^3-4\right)\)

\(\Leftrightarrow3^x\cdot3^3-4\cdot3^x=3^{13}\left(3^3-4\right)\)

\(\Leftrightarrow3^x\left(3^3-4\right)=3^{13}\left(3^3-4\right)\)

\(\Leftrightarrow3^x=3^{13}\Leftrightarrow x=13\)

a. x=8

b. x=13

còn cách tính thì mình quên rồi vì minh học cái này lâu lắm rồi ko nhớ đc.

Lời giải:

$3^{x-1}+4.3^{x-2}=\frac{7}{243}$
$\Leftrightarrow 3. 3^{x-2}+4.3^{x-2}=\frac{7}{243}$

$\Leftrightarrow 3^{x-2}(3+4)=\frac{7}{243}$

$\Rightarrow 3^{x-2}=\frac{1}{243}=3^{-5}$

$\Rightarrow x-2=-5$

$\Rightarrow x=-3$

\(3^{x-1}+4.3^{x-2}=\frac{7}{243}\)

\(\Rightarrow3^1.3^{x-2}+4.3^{x-2}=\frac{7}{243}\)

\(\Rightarrow3^{x-2}.\left(3^1+4\right)=\frac{7}{243}\)

\(\Rightarrow3^{x-2}.7=\frac{7}{243}\)

\(\Rightarrow3^{x-2}=\frac{7}{243}:7\)

\(\Rightarrow3^{x-2}=\frac{1}{243}\)

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

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

\(\Rightarrow x=\left(-5\right)+2\)

\(\Rightarrow x=-3\)

Vậy \(x=-3.\)

Chúc bạn học tốt!

\(\frac{x}{7}=\frac{y}{3}=\frac{x-y}{7-3}=\frac{20}{4}=5\)

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

\(\frac{y}{3}=5\Rightarrow y=15\)

tíc mình nha

3 bài à

1/  ta có x/7 = y/3 và x-y=20

ADTCDTSBN

x/7=y/3 = x-y/ 7-3 = 20/4= 5

Suy ra

x/7=5 => x=7.5= 35

y/3=5=> y= 3.5 = 15

Vậy x = 35 và y=15

2/ 3^x-3.9= 729

3^x-3 . 3²=(3²)³

x-3 .2=6

x-3 = 6:2 

x-3= 3

x= 3+3 

x=6

Nhu lon

\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}\left(5-3\right)=2.5^{11}\)

\(5^{x+3}.2=2.5^{11}\)

\(5^{x+3}=5^{11}\)

\(x+3=11\)

\(x=8\)

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(4^{x+1}\left(4^2-3\right)=13.4^{11}\)

\(4^{x+1}.13=13.4^{11}\)

\(4^{x+1}=4^{11}\)

\(x+1=11\)

\(x=10\)

114635262 nhé bn

Tk mình đi !

2121390/2121309=1

KQ=1165795659

minh tinh may tinh ko sai dau

k cho minh nhe

a)\(\left(\frac{1}{2}-\frac{1}{3}\right).6^x+6^{x+2}=6^{15}+6^{18}\)

\(\frac{1}{6}.6^x+6^{x+2}=6^{15}\left(1+6^3\right)\)

\(\frac{1}{6}.6^x\left(1+6^3\right)=6^{15}.217\)

\(6^{x-1}.217=6^{15}.217\)

\(6^{x-1}=6^{15}\)

\(x-1=15\)

\(x=16\)

b) \(\left(\frac{1}{2}-\frac{1}{6}\right).3^{x+4}-4.3^x=3^{16}-4.3^{13}\)

\(\frac{1}{3}.3^x.4\left(3^4-1\right)=3^{13}.4\left(3^3-1\right)\)

\(3^x.4.\left(3^3-1\right)=3^{13}.4.\left(3^3-1\right)\)

\(3^x=3^{13}\)

\(x=13\)

\(\left(\frac{1}{2}-\frac{1}{6}\right).\left(3^x.3^4\right)-4.3^x=3^{16}-4.3^{13}\)

=> \(\frac{1}{3}.3^x.3^4-4.3^x=3^{16}-4.3^{13}\)

=> \(3^x.3^4-4.3^x=\left(3^{16}-4.3^{13}\right):\frac{1}{3}\)

=> \(3^x.3^4-4.3^x=-386339074,3\)

=> \(3^x.\left(3^4-4\right)=-386339074,3\)

=> \(3^x.77=-386339074,3\)

=> \(3^x=-386339074,3:77\)

=> \(3^x=-5017390,575\)

=> x = ... chắc tự ngồi tính đc

cái a tương tự thôi

\(\left(\frac{3^x}{3}\right)^2=\frac{1}{729}\Rightarrow3^{x-1}=\frac{1}{27}\Rightarrow x-1=-3\Rightarrow x=-2\)

\(x=-2\)

x = -2 nhé bn

tích mk nha các bn

>_< học tốt