Mathematics: Solve for x. 8^2x −3 = ( 1 16 )^x − 2 plz

Solve for x. 8^2x −3 = ( 1 16 )^x − 2 plz

Ответ:

tylerbrewton23

07.01.2022

$\large\boxed{x=\dfrac{17}{10}=1.7}$

Step-by-step explanation:

$8=2^3\\\\\dfrac{1}{16}=\dfrac{1}{2^4}=2^{-4}\qquad\text{used}\ a^{-n}=\dfrac{1}{a^n}\\\\8^{2x-3}=\left(\dfrac{1}{16}\right)^{x-2}\\\\(2^3)^{2x-3}=(2^{-4})^{x-2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(2x-3)}=2^{-4(x-2)}\iff3(2x-3)=-4(x-2)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\(3)(2x)+(3)(-3)=(-4)(x)+(-4)(-2)\\\\6x-9=-4x+8\qquad\text{add 9 to both sides}\\\\6x=-4x+17\qquad\text{add 4x to both sides}\\\\10x=17\qquad\text{divide both sides by 10}\\\\x=1.7$

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Ответ:

dntestkly4581

01.11.2021

Mathematics

1) The top right corner of the rectangle is (c,b). The bottom left corner of the rectangle is (a,d)

2) The width of the rectangle is the same as the height of the rectangle. The top of the rectangle is "b" high and the bottom of the rectangle is "d" low, so the width is simply the difference, "b - d"

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Solve for x. 8^2x −3 = ( 1 16 )^x − 2 plz

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