\(4^n=4096\\ \Leftrightarrow2^{2n}=2^{12}\\ \Leftrightarrow2n=12\\ \Leftrightarrow n=6\\ 5^n=15625=5^6\\ \Leftrightarrow n=6\\ 6^{n+3}=216=6^3\\ \Leftrightarrow n+3=3\\ \Leftrightarrow n=0\\ 4^{n-1}=1024=4^5\\ \Leftrightarrow n-1=5\\ \Leftrightarrow n=6\)

`54+4x=10^2-18`

`54+4x=100-18`

`54+4x=82`

`4x=82-54=28`

`x=28:4=7`

7

`54 + 4x = 10^2 - 18`

`54 + 4x = 82`

`4x = 28`

`x = 7`

\(54+4x=10^2-18< =>4x=10^2-18-54< =>4x=28< =>x=7\)

`245-4[2^4:2^3+2(4.3^2-9)]-5`

`=245-4[2^[4-3]+2(36-9)]-5`

`=245-4(2+2.27)-5`

`=245-4(2+54)-5`

`=245-4.56-5`

`=245-224-5`

`=21-5`

`=16`

\(=245-4\left[2+2\left(4\cdot3^2-9\right)\right]-5=245-4\left[2+2\cdot27\right]-5=245-4\cdot56-5=16\)

`245-4[2^4:2^3+2(4.3^2-9)]-5`

`=245-4[2^[4-3]+2(36-9)]-5`

`=245-4(2+2.27)-5`

`=245-4(2+54)-5`

`=245-4.56-5`

`=245-224-5`

`=21-5`

`=16`

`x^2021=x^2022`

`x^2021-x^2022=0`

`x^2021(1-x)=0`

`@TH1:x^2021=0=>x=0`

`@TH2:1-x=0=>x=1`

`54.178+178.19-78.73`

`=178.(54+19)-78.73`

`=178.73-78.73`

`=73.(178-78)`

`=73.100=7300`

$54.178+178.19-78.73$

$=178.(54+19)-78.73$

$=178.73-78.73$

$=73.(178-78)$

$=73.100=7300$

`915-643+185:5-195:13`

`=915-643+37-15`

`=272+37-15`

`=309-15`

`=294`

\(915-643+185\div5-195\div13\)

\(=915-643+37-15\)

\(=272+22\)

\(=294\)

Điều kiện: \(x\in\mathbb N^*\).

Số số hạng: \(\left(x-2\right):2+1\) (số)

Tổng dãy số: \(\dfrac{\left(x+2\right)\left[\left(x-2\right):2+1\right]}{2}=2450\)

\(\left(x+2\right)\left[\left(x-2\right):2+1\right]=4900\)

\(\left(x+2\right)\cdot\dfrac{1}{2}x=4900\)

\(\dfrac{1}{2}x^2+x-4900=0\)

\(\left[{}\begin{matrix}x=98\left(TM\right)\\x=-100\left(L\right)\end{matrix}\right.\)

Vậy \(x=98\).

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