Mathematics: Which equation is equivalent to 2^4x = 8^x-3

Which equation is equivalent to 2^4x = 8^x-3

Ответ:

vanleervanleer

12.03.2022

x = -9

Step-by-step explanation:

$8=2^3\\\\8^{x-3}=(2^3)^{x-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\8^{x-3}=2^{3(x-3)}\qquad\text{use the distribtutive property}\ a(b+c)=ab+ac\\\\8^{x-3}=2^{3x-9}\\\\\text{Therefore}\\\\2^{4x}=8^{x-3}\Rightarrow2^{4x}=2^{3x-9}\iff4x=3x-9\qquad\text{subtract}\ 3x\ \text{from both isdes}\\\\4x-3x=3x-3x-9\\\\x=-9$

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Ответ:

urgurlkitty

09.04.2023

Mathematics

If the question is how many shelves are needed, then the answer is 18 shelves.

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Which equation is equivalent to 2^4x = 8^x-3

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