I want to solve this equation: $(0.2)^{(-x+3)}=125^{(2x+3)}$.
The correct answer is $-2.4$, however I end up getting $12$.
I'm following these steps:
$(0.2)^{(-x+3)}=125^{(2x+3)}$
$125^{(3x-9)}=125^{(2x+3)}$
$3x-9=2x+3$
$x=12$
How do I solve this equation: $(0.2)^{(-x+3)}=125^{(2x+3)}$
0
$\begingroup$
inequality
exponential-function
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0Can you explain me why $0.2^{-x+3} = 125^{3x - 9}$ ? When you pass from first to second line. – 2017-02-14
1 Answers
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Note that $0.2=\frac15=5^{-1}$. So we have: $$(5^{-1})^{3-x}=(5^3)^{2x+3} \Rightarrow 5^{x-3}=5^{6x+9}$$
and that's equivalent to $x-3=6x+9$.
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0Okay, thanks! However why isn't it possible to say 0.2=125^-3 – 2017-02-14
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1Because it's not true: $125^{-3}=\frac{1}{125^3}$. You were trying to say $$0.2=125^{-\frac13}=\frac{1}{125^{\frac13}}=\frac{1}{\sqrt[3]{125}}=\frac15$$ and that is correct. You're welcome~ – 2017-02-14
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0Sorry, I meant 0.2^-3 = 125 – 2017-02-14
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0You can, but you will have to as is follows: $$0.2=(0.2)^{-3\cdot \frac{-1}{3}}=((0.2)^{-3})^{\frac{-1}{3}}=125^{\frac{1}{3}}$$ so $0.2^{3-x}=125^{\frac{3-x}{-3}}$. – 2017-02-14
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0Okay, thanks a lot! – 2017-02-14