`@` `\text {Ans}`
`\downarrow`
`a)`
`4^n = 256`
`=> 4^n = 4^4`
`=> n=4`
Vậy, `n=4`
`b)`
\(9^{5n-8}=81\)
`=> 9^(5n-8) = 9^2`
`=> 5n-8=2`
`=> 5n = 10`
`=> n=2`
Vậy, `n=2`
`c)`
\(3^{n+2}\div27=3\)
`=> 3^(n+2) = 3* 27`
`=> 3^(n+2) = 3*3^3`
`=> 3^(n+2) = 3^4`
`=> n+2=4`
`=> n=4-2`
`=> n=2`
Vậy, `n=2`
`d)`
\(8^{n+2}\cdot2^3=8^5\)
`=> 8^(n+2) *8 = 8^5`
`=> 8^(n+2) = 8^5 \div 8`
`=> 8^(n+2) = 8^4`
`=> n+2=4`
`=> n=2`
Vậy. `n=2`
`e)`
\(3^{n-5}=27^4\)
`3^(n-5) = 3^12`
`=> n-5=12`
`=> n=12 + 5`
`=> n=17`
Vậy, `n=17`
`f)`
\(16^{n+3}\cdot2^4=\left(16^3\right)^4\)
`=> 16^(n+3)*16 = 16^12`
`=> 16^(n+3+1) = 16^12`
`=> n+3+1 = 12`
`=> n+4 = 12`
`=> n=12 - 4`
`=> n=8`
Vậy, `n=8`
_________
`a)`
\(30-2x^2=12\)
`=> 2x^2 = 30 - 12`
`=> 2x^2 = 18`
`=> x^2 = 18 \div 2`
`=> x^2 = 9`
`=> x^2 = (+-3)^2`
`=> x = +-3`
Vậy, `x \in {3; -3}`
`b)`
\(\left(9-2x\right)^3=125\)
`=> (9-2x)^3 = 5^3`
`=> 9-2x = 5`
`=> 2x = 9-5`
`=> 2x=4`
`=> x=2`
Vậy, `x=2`
`c)`
\(\left(2x-2\right)^4=0\)
`=> 2x-2 = 0`
`=> 2x=2`
`=> x=1`
Vậy, `x=1`
`d)`
\(\left(x+5\right)^3=\left(2x\right)^3\)
`=> x+5 = 2x`
`=> x + 5 - 2x =0`
`=> (x-2x) + 5 = 0`
`=> -x + 5 = 0`
`=> -x = -5`
`=> x=5`
Vậy, `x=5`
`e)`
\(\left(5x-1\right)^3=8^2\)
`=> (5x-1)^3 = 4^3`
`=> 5x-1 = 4`
`=> 5x = 4+1`
`=> 5x = 5`
`=> x=1`
Vậy, `x=1`
`f)`
\(5^x+15=2^3\cdot5\)
`=> 5^x + 15 = 40`
`=> 5^x = 40 - 15`
`=> 5^x = 25`
`=> 5^x = 5^2`
`=> x=2`
Vậy, `x=2`
`@` `\text {Kaizuu lv uuu}`
a) \(30-2x^2=12\)
\(\Rightarrow2x^2=30-12\)
\(\Rightarrow2x^2=18\)
\(\Rightarrow x^2=\dfrac{18}{2}=9\)
\(\Rightarrow x^2=3^2\)
\(\Rightarrow x=\pm3\)
b) \(\left(9-2x\right)^3=125\)
\(\Rightarrow\left(9-2x\right)^3=5^3\)
\(\Rightarrow9-2x=5\)
\(\Rightarrow2x=9-5\)
\(\Rightarrow x=\dfrac{4}{2}=2\)
c) \(\left(2x-2\right)^4=0\)
\(\Rightarrow\left(2x-2\right)^4=0^4\)
\(\Rightarrow2x-2=0\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=1\)
d) \(\left(x+5\right)^3=\left(2x\right)^3\)
\(\Rightarrow x+5=2x\)
\(\Rightarrow2x-x=5\)
\(\Rightarrow x=5\)
e) \(\left(5x-1\right)^3=8^2\)
\(\Rightarrow\left(5x-1\right)^3=\left(2^3\right)^2\)
\(\Rightarrow\left(5x-1\right)^3=2^6\)
\(\Rightarrow5x-1=2^2\)
\(\Rightarrow5x-1=4\)
\(\Rightarrow5x=5\)
\(\Rightarrow x=1\)
f) \(5^x+15=2^3\cdot5\)
\(\Rightarrow5^x+15=8\cdot5\)
\(\Rightarrow5^x+15=40\)
\(\Rightarrow5^x=40-15=25\)
\(\Rightarrow5^x=5^2\)
\(\Rightarrow x=2\)
10:
a: 4^n=256
=>4^n=4^4
=>n=4
b: 9^5n-8=81
=>5n-8=2
=>5n=10
=>n=2
c: 3^n-5=27^4=3^12
=>n-5=12
=>n=17
d: 3^n+2:27=3
=>3^n+2=81
=>n+2=4
=>n=2
e: =>2^(3n+6)*2^3=2^15
=>3n+9=15
=>3n=6
=>n=3
f: =>2^(4n+12)*2^4=(2^12)^4=2^48
=>4n+16=48
=>4n=32
=>n=8
a) \(4^n=256\)
\(\Rightarrow4^n=4^4\)
\(\Rightarrow n=4\)
b) \(9^{5n-8}=81\)
\(\Rightarrow9^{5n-8}=9^2\)
\(\Rightarrow5n-8=2\)
\(\Rightarrow5n=10\)
\(\Rightarrow n=2\)
c) \(3^{n+2}:27=3\)
\(\Rightarrow3^{n+2}:3^3=3\)
\(\Rightarrow3^{n+2-3}=3^1\)
\(\Rightarrow3^{n-1}=3^1\)
\(\Rightarrow n-1=1\)
\(\Rightarrow n=2\)
d) \(8^{n+2}\cdot2^3=8^5\)
\(\Rightarrow8^{n+2}\cdot8=8^5\)
\(\Rightarrow8^{n+2+1}=8^5\)
\(\Rightarrow n+3=5\)
\(\Rightarrow n=2\)
e) \(3^{n-5}=27^4\)
\(=3^{n-1}=\left(3^3\right)^4\)
\(\Rightarrow3^{n-1}=3^{12}\)
\(\Rightarrow n-1=12\)
\(\Rightarrow n=13\)
f) \(16^{n+3}\cdot2^4=\left(16^3\right)^4\)
\(\Rightarrow16^{n+3}\cdot16=16^{12}\)
\(\Rightarrow16^{n+3+1}=16^{12}\)
\(\Rightarrow n+4=12\)
\(\Rightarrow n=8\)
