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1, 4\(^{x+1}\) + 4\(^0\) = 65
\(\Rightarrow\)4\(^{x+1}\) = 65 - 1
\(\Rightarrow\)x + 1 = 64 : 4
\(\Rightarrow\)x + 1 = 16
\(\Rightarrow\)x = 15
2) 10 + 2x = 16\(^{^2}\): 4\(^3\)
\(\Rightarrow\)10 + 2x = 4
\(\Rightarrow\)2x = 4 - 10
\(\Rightarrow\)2x = -6
\(\Rightarrow\)x = -3
Lời giải:
a.
$4(2x-4)+2=18$
$4(2x-4)=16$
$2x-4=16:4=4$
$2x=4+4=8$
$x=8:2$
$x=4$
b.
\(5^3+(18x-65).3=26^2+10\)
$125+3(18x-65)=686$
$3(18x-65)=686-125=561$
$18x-65=561:3=187$
$18x=187+65$
$18x=252$
$x=252:18=14$
c.
\(|x-10|+2^2.5=5^5\)
$|x-10|+20=3125$
$|x-10|=3125-20=3105$
$\Rightarrow x-10=3105$ hoặc $x-10=-3105$
$\Rightarrow x=3115$ hoặc $x=-3095$
d.
\((x-2)^2-2^3.5=104\)
$(x-2)^2-40=104$
$(x-2)^2=104+40=144=12^2=(-12)^2$
$\Rightarrow x-2=12$ hoặc $x-2=-12$
$\Rightarrow x=14$ hoặc $x=-10$
a) pt <=> \(\frac{x\left(x+1\right)}{2}=500500\)
<=> \(x^2+x=1001000\)
<=> \(x^2-1000x+1001x-1001000=0\)
<=> \(\left(x-1000\right)\left(x+1001\right)=0\)
<=> \(\orbr{\begin{cases}x=1000\\x=-1001\end{cases}}\)
Do \(x>0\)=> \(x=1000\)
b)
<=> \(2x=210\)
<=> \(x=105\)
c)
<=> \(6x-81=3.7\)
<=> \(x=17\)
d)
<=> \(125-5\left(3x-1\right)=5^2\)
<=> \(5\left(3x-1\right)=100\)
<=> \(3x-1=20\)
<=> \(x=7\)
e)
<=> \(4^{x+1}+1=65\)
<=> \(4^{x+1}=64\)
<=> \(x+1=3\)
<=> \(x=2\)
j)
<=> \(2\left(2x-3\right)=14\)
<=> \(2x-3=7\)
<=> \(x=5\)
a,10+2x=45:43
10+2x=42
10+2x=16
2x=16-10
2x=6
x=6:2
x=3
b,310-(20-x)=300
20-x =310-300
20-x =10
x=20-10
x=10
c,4x+1+40=65
4x+1+40=65
4x+1+1 =65
4x+1 =65-1
4x+1 =64
4x+1 =43
x =3-1
=> x =2
a) 10 + 2x = 45 : 43
10 + 2x = 42 = 16
2x = 16 - 10
2x = 6
x = 3
b) 310 - (20 - x) = 300
310 - 20 + x = 300
290 + x = 300
x = 300 - 290
x = 10
c) 4x + 1 + 40 = 65
4x + + 1 = 65
4x + 1 = 64 = 43
=> x + 1 = 3
=> x = 2