How to find x in an exponential equation

1 answer:

5 0

If the bases are the same then you can let the exponents be equal to each other. If the exponents are not the same then you will have to use logarithms to solve for x.

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Which equation is the inverse of 2(x - 2)^3=8(7+y)

irina1246 [14]

Answer:

$\large\boxed{y=2\pm\sqrt{28+4x}}$

Step-by-step explanation:

$2(x-2)^2=8(7+y)\\\\\text{exchange x to y, and vice versa:}\\\\2(y-2)^2=8(7+x)\\\\\text{solve for y:}\\\\2(y-2)^2=(8)(7)+(8)(x)\\\\2(y-2)^2=56+8x\qquad\text{divide both sides by 2}\\\\(y-2)^2=28+4x\iff y-2=\pm\sqrt{28+4x}\qquad\text{add 2 to both sides}\\\\y=2\pm\sqrt{28+4x}$

6 0

3 years ago

Read 2 more answers

Which equation does the graph of the systems of equations solve?

mihalych1998 [28]

Answer:

$\text{B. }\frac{1}{3}x-3=-x+1$

Step-by-step explanation:

Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to $(x_1,y_1)$ and $(x_2, y_2)$ (doesn't matter which you assign) and use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let:

$(x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)$

The slope is equal to:

$m=\frac{0-1}{1-0}=\frac{-1}{1}=-1$

Therefore, the slope of this line is -1. In slope-intercept form $y=mx+b$ , $m$ represents slope, so one of the lines must have a term with $-x$ in it, which eliminates answer choices A and D.

For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:

$(x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)$

Using the slope formula:

$m=\frac{-2-(-3)}{3-0}=\frac{1}{3}$

Thus, the slope of the line is 1/3 and the other line must have a term with $\frac{1}{3}x$ in it, eliminating answer choice C and leaving the answer $\boxed{\text{B. }\frac{1}{3}x-3=-x+1}$