Answer:
n = 11.
Step-by-step explanation:
2 ^ n / 2 = 1024
Multiply both sides by 2:
2^n = 2048
log 2^n = log 2048
n log 2 = log 2024
n = log 2048 / log 2
= 11 (answer).
Answer:
![\boxed{x^{\frac{21}{5}}}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%5E%7B%5Cfrac%7B21%7D%7B5%7D%7D%7D)
Step-by-step explanation:
![\left(\sqrt[5]{x^{7}} \right)^{3}](https://tex.z-dn.net/?f=%5Cleft%28%5Csqrt%5B5%5D%7Bx%5E%7B7%7D%7D%20%5Cright%29%5E%7B3%7D)
Start inside the parentheses. Recall that
![\sqrt[5]{x^{7}} = \left(x^{7}\right)^{\frac{1}{5}}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E%7B7%7D%7D%20%3D%20%5Cleft%28x%5E%7B7%7D%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D)
According to the laws of exponents, when you have an exponent raised to a power, you multiply the exponents. So,
![\left(x^{7}\right)^{\frac{1}{5}} = x ^{\frac{7}{5}}](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B7%7D%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%20%3D%20x%20%5E%7B%5Cfrac%7B7%7D%7B5%7D%7D)
At this point, we have
![\left(\sqrt[5]{x^{7}} \right)^{3} = \left(x^{\frac{7}{5}}\right)^{3}](https://tex.z-dn.net/?f=%5Cleft%28%5Csqrt%5B5%5D%7Bx%5E%7B7%7D%7D%20%5Cright%29%5E%7B3%7D%20%3D%20%5Cleft%28x%5E%7B%5Cfrac%7B7%7D%7B5%7D%7D%5Cright%29%5E%7B3%7D)
Now, when we remove the parentheses, we multiply the exponents again. The result is
![\left(\sqrt[5]{x^{7}} \right)^{3} = \boxed{x^{\frac{21}{5}}}](https://tex.z-dn.net/?f=%5Cleft%28%5Csqrt%5B5%5D%7Bx%5E%7B7%7D%7D%20%5Cright%29%5E%7B3%7D%20%3D%20%5Cboxed%7Bx%5E%7B%5Cfrac%7B21%7D%7B5%7D%7D%7D)
Answer:
Any number other than 2
Step-by-step explanation:
First, solve the equation
4x +3 = 11
Subtract 3 on both sides
4x=8
Divide by 4 on both sides
x=2
Since 2 is the solution, any number other than 2 would make the equation false
Hope this helps! :)
Answer: (just the first question)
x=3
y=17
Step-by-step explanation:
3x+8=-5x+32
add 5x and subtract 8 from both sides
8x=24
divided by 8
x=3
substitute+simplify
y=3x+8
y=9+8
y=17
y=-5x+32
y=-15+32
y=17