Bài 1:

a) \(4^{x+2}+4^x=68\)

\(\Rightarrow4^x\cdot\left(4^2+1\right)=68\)

\(\Rightarrow4^x\cdot17=68\)

\(\Rightarrow4^x=\dfrac{68}{17}\)

\(\Rightarrow4^x=4\)

\(\Rightarrow4^x=4^1\)

\(\Rightarrow x=1\)

b) \(5\cdot2^{x+4}-3\cdot2^x=308\)

\(\Rightarrow2^x\cdot\left(5\cdot2^4-3\right)=308\)

\(\Rightarrow2^x\cdot\left(5\cdot16-3\right)=308\)

\(\Rightarrow2^x\cdot77=308\)

\(\Rightarrow2^x=\dfrac{308}{77}\)

\(\Rightarrow2^x=4\)

\(\Rightarrow2^x=2^2\)

\(\Rightarrow x=2\)

c) \(4\cdot3^{x+1}+7\cdot3^x=513\)

\(\Rightarrow3^x\cdot\left(4\cdot3+7\right)=513\)

\(\Rightarrow3^x\cdot19=513\)

\(\Rightarrow3^x=\dfrac{513}{19}\)

\(\Rightarrow3^x=27\)

\(\Rightarrow3^x=3^3\)

\(\Rightarrow x=3\)

d) \(5^{x+4}-5^x=3120\)

\(\Rightarrow5^x\cdot\left(5^4-1\right)=3120\)

\(\Rightarrow5^x\cdot\left(625-1\right)=3120\)

\(\Rightarrow5^x\cdot624=3120\)

\(\Rightarrow5^x\cdot\dfrac{3120}{624}\)

\(\Rightarrow5^x=5\)

\(\Rightarrow5^x=5^1\)

\(\Rightarrow x=1\)

f) \(3\cdot4^{2x+1}-16^x=2816\)

\(\Rightarrow3\cdot4^{2x+1}-\left(4^2\right)^x=2816\)

\(\Rightarrow3\cdot4^{2x+1}-4^{2x}=2816\)

\(\Rightarrow4^{2x}\cdot\left(3\cdot4-1\right)=2816\)

\(\Rightarrow4^{2x}\cdot11=2816\)

\(\Rightarrow4^{2x}=\dfrac{2816}{11}\)

\(\Rightarrow4^{2x}=256\)

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

\(\Rightarrow2^{4x}=2^8\)

\(\Rightarrow4x=8\)

\(\Rightarrow x=2\)

Bài 2:

\(2^x+124=5^y\)

\(\Rightarrow5^y-2^x=124\)

\(\Rightarrow5^y-2^x=125-1\)

\(\Rightarrow\left\{{}\begin{matrix}5^y=125\\2^x=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}5^y=5^3\\2^x=2^0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}y=3\\x=0\end{matrix}\right.\)

Vậy: .... 

bạn ghi lại đề được ko

a: \(16^x< 32^4\)

=>\(2^{4x}< 2^{20}\)

=>4x<20

=>\(x< 5\)

=>0<=x<5

=>\(x\in\left\{0;1;2;3;4\right\}\)

b: \(9< 3^x< 81\)

=>\(3^2< 3^x< 3^4\)

=>2<x<4

=>x=3

c: \(25< 5^x< 125\)

=>\(5^2< 5^x< 5^3\)

=>2<x<3

mà x là số tự nhiên

nên \(x\in\varnothing\)

∅ này là j v ạ

\(2^x+3\cdot2^x=9\cdot2^9\)

\(\Rightarrow2^x\cdot\left(1+3\right)=9\cdot2^9\)

\(\Rightarrow2^x\cdot4=9\cdot2^9\)

\(\Rightarrow2^x=\dfrac{9\cdot2^9}{4}\)

\(\Rightarrow2^x=9\cdot2^7\)

Xem lại đề ! 

tại em đang dùng pc mà khum bt nhấn đou á camon nha

\(4\times x^3+15=47\)

\(4\times x^3=32\)

\(x^3=8\)

\(x=2\)

toán lp 5 ak bn ? dễ quá ha --_--''

\(a,TH1:x-2021=0=>x=2021\)

\(Th2:x-2022=0=>x=2022\)

Vậy \(x\in\left\{2021;2022\right\}\)

\(b,x\left(8-5\right)=1080\)

\(x.3=1080\)

\(x=360\)

\(c,x^3=216< =>6^3=216=>x=3\)

\(d,5^5=3125\)

a)  ( x- 2021) * ( x- 2022) = 0

=>  \(\orbr{\begin{cases}x-2021=0\\x-2022=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2021\\x=2022\end{cases}}}\)

b)  b. 8x - 5x = 2022

=>  3x  =  2022

=>  x  =   674

c)  \(5\cdot x^3=1080\)

=>  \(x^3=216\)

=>  \(x^3=6^3\)

=>   x  =  6

d)   \(5^x=3125\)

=>    \(5^x=5^5\)

=>  x    =  5

a) 27 . 75 + 25 .27 - 150 = 27 . (75 + 25) - 150

                                       = 270 . 100 - 150

                                       = 27 000 - 150

                                       = 26 850

b) 3.5² - 16 : 2² = 12,25 - 16 : 4

                         = 12,25 - 4

                        = 8,25

c) 20 - [30 - (5 - 1)² ] = 20 - [30 - 4² ]

                                 = 20 - 30 - 16

                                 = (-10) - 16

                                = -26

d) 60 : {[(12 - 3) . 2] + 2} = 60 : {[9 . 2] + 2}

                                       = 60 : {18 + 2}

                                      = 60 : 20

                                      = 3

\(a)\)\(\left(50-6.x\right).18=2^3.3^2.5\)

\(\Leftrightarrow\)\(\left(50-6.x\right).18=8.9.5\)

\(\Leftrightarrow\)\(\left(50-6.x\right).18=360\)

\(\Leftrightarrow\)\(\left(50-6.x\right)=360\div18\)

\(\Leftrightarrow\)\(50-6.x=20\)

\(\Leftrightarrow\)\(6.x=50-20\)

\(\Leftrightarrow\)\(6.x=30\)

\(\Leftrightarrow\)\(x=5\)

\(b)\)\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=7450\)

\(\Leftrightarrow\)\(100x+\left(1+2+3+...+100\right)=7450\)

\(\Leftrightarrow\)\(100x+5050=7450\)

\(\Leftrightarrow\)\(100x=7450-5050\)

\(\Leftrightarrow\)\(100x=2400\)

\(\Leftrightarrow\)\(x=24\)

b.

(x+1)+(x+2)+...+(x+100)=7450

=> 100x + (1+2+3+...+100)=7450

=>100x + (100+1).50=7450

=>100x=2400

=>x=24