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2 years ago

If 2^2x= 8^x-1 what is the value of x?

Mathematics

2 answers:

Alja [10]2 years ago

8 0

2^(2x) = 2^(3x - 3)
2x = 3x - 3 
3 = x

arlik [135]2 years ago

7 0

Solutions

$2^(2x) = 2^(3x - 3) 

2x = 3x - 3 

3 = x

x = 3$

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Solve the following system of equations 2x – 3y = 6 4x+2y=4

FinnZ [79.3K]

Answer:

$\boxed{(\frac{3}{2} ,-1)}$

Step-by-step explanation:

$\left \{ {{2x-3y=6} \atop {4x+2y=4}} \right.$

It seems this system of equations would be solved easier using the elimination method (the x and y values are lined up).

Multiply everything in the first equation by -2 (we want the 4x to be able to cancel out with a -4x).

$2x-3y=6 \rightarrow -4x+6y=-12$

Now line up the equations (they are already lined up - convenient) and add them from top to bottom.

$\left \{ {{-4x+6y=-12} \atop {4x+2y=4}} \right.$

The -4x and 4x are opposites, so they cancel out.

Adding 6y and 2y gives you 8y, and adding -12 and 4 gives you -8.

$8y=-8$

Divide both sides by 8.

$y=-1$

Since you have the y-value you can substitute this in to the second (or first equation, it doesn't necessarily matter) equation.

$4x +2(-1)=4$

Simplify.

$4x -2=4$

Add 2 to both sides.

$4x=6$

Divide both sides by 4.

$x=\frac{6}{4} \rightarrow\frac{3}{2}$

The final answer is $x=\frac{3}{2} ,~y=-1$ .

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2 years ago

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Mashutka [201]

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$x^4-81=0\\\\Factor:\\(x^2-9)(x^2+9)=0\\(x-3)(x+3)(x^2+9)=0\\\\\text{Apply the Zero Product Property:}\\x-3=0\qquad x+3=0\qquad x^2+9=0\\\boxed{x=3}\qquad \qquad \boxed{x=-3}\qquad \quad x^2=-9\\.\qquad \qquad \qquad \qquad \qquad \qquad x=\sqrt{-9}\\.\qquad \qquad \qquad \qquad \qquad \qquad \boxed{x=\pm 3i}$

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2 years ago