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Angelina_Jolie [31]
3 years ago
15

Solve the equation 3^(2x) -4*3^(x+1) + 27 = 0. use rules of exponents to change 3^(x+1)​

Mathematics
1 answer:
Leviafan [203]3 years ago
4 0

Answer:

\huge\boxed{x=1\ \vee\ x=2}

Step-by-step explanation:

3^{2x}-4\cdot3^{x+1}+27=0\\\\\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\\left(3^x\right)^2-4\cdot3^x\cdot3^1+27=0\\\\\left(3^x\right)^2-12\cdot3^x+27=0\\\\\text{substitute}\ 3^x=t>0\\\\t^2-12t+27=0\\\\t^2-3t-9t+27=0\\\\t(t-3)-9(t-3)=0\\\\(t-3)(t-9)+0\iff t-3=0\ \vee\ t-9=0\\\\t-3=0\qquad\text{add 3 to both sides}\\\boxed{t=3}\\\\t-9=0\qquad\text{add 9 to both sides}\\\boxed{t=9}

\text{We return to substitution:}\\\\3^x=t\\\\3^x=3\ \vee\ 3^x=9\\\\3^x=3^1\ \vee\ 3^x=3^2\\\\\boxed{x=1}\ \vee\ \boxed{x=2}

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Precalc help needed, find g ° f!
Nezavi [6.7K]

Answer:

g o f = -[f(x)]² + 3 = -(|x|)² + 3 = -x² + 3 = g(x)

Step-by-step explanation:

g o f = g [ f(x) ]

This means replace the x of g(x) with f(x):

g o f = -[f(x)]² + 3 = -(|x|)² + 3

As x² ≥ 0 for any value of x (whether it be positive or negative), then -(|x|)² + 3 = -x² + 3 = g(x)

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8 0
2 years ago
Simplify (2^5/3^2)^4 I need help asap within 10 min
Daniel [21]

Answer:

\frac{2^{20} }{3^{8} }

Step-by-step explanation:

Exponent Multiplication Rule :

(\frac{x^{a} }{y^{b} } )^{c} = \frac{x^{ac} }{y^{bc} }

=============================================================

Solving :

⇒ (\frac{2^{5} }{3^{2} } )^{4}

⇒ \frac{2^{5(4)} }{3^{2(4)} }

⇒ \frac{2^{20} }{3^{8} }

3 0
2 years ago
Is this the most simplified version?
Nonamiya [84]
Yes it is the most simplified version
6 0
3 years ago
Consider the following function:<br> f(x) = 2x/3x^2-3 What is the domain of the function?
gulaghasi [49]

Answer:

all real numbers except -1 and 1

Next question is the first two boxes “infinity & negative infinity” on edge.

For the first part it is D and for the second part it is A and B on edge 2020

mark me brinilylist

4 0
2 years ago
F(x) = -x^2 + 6x + 4 find f(-7)
mylen [45]

Answer:

11

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-(-7)^2 + (6*-7) + 4

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