$\bf 5^{x+3}=\cfrac{1}{125}\implies 5^{x+3}=\cfrac{1}{5^3}\implies 5^{x+3}=5^{-3}
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\textit{because the bases are the same, the exponents must also be the same}
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x+3=-3\implies \boxed{x=-6}\\\\
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3^x=4^{2x}\implies log(3^x)=log(4^{2x})\implies xlog(3)=(2x)log(4)
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\cfrac{x}{2x}=\cfrac{log(4)}{log(3)}\implies \cfrac{1}{x}=\cfrac{log(4)}{log(3)}\implies \cfrac{log(3)}{log(4)}=x\implies \boxed{0.79248125\approx x}$

6 0

2 years ago

Find the second derivative, do not have to simplify

zlopas [31]

$f(x)=\sec(\pi x)=\dfrac{1}{\cos(\pi x)}=[\cos(\pi x)]^{-1}\\\\\text{use}\\\\(a^n)'=na^{n-1}\\\\(\cos x)'=-\sin x\\\\f'(g(x))=f'(g(x))\cdot g'(x)$

$f'(x)=\left\{[\cos(\pi x)]^{-1}\right\}'=-[\cos(\pi x)]^{-2}\cdot[-\sin(\pi x)]\cdot\pi\\\\=\dfrac{\pi\sin(\pi x)}{[\cos(\pi x)]^2}=\pi\dfrac{\sin(\pi x)}{\cos(\pi x)}\cdot\dfrac{1}{\cos(\pi x)}\\\\=\pi\tan(\pi x)\sec(\pi x)$

6 0

2 years ago

There are 7 rows of chairs and each row has 12 chairs in them; how many chairs are there altogether?

anyanavicka [17]

Answer:

184

Step-by-step explanation:

Just multiply 12 by 7

4 0

2 years ago

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