Solve each equation. 10-2log9(1/4x)=9

Mathematics

1 answer:

jenyasd209 [6]3 years ago

3 0

Answer:

Step-by-step explanation:

$Domain:\ \dfrac{1}{4}x>0\to x>0\\\\Use:\ \log_ab=c\iff a^c=b\ for\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\\====================================$

$10-2\log_9\left(\dfrac{1}{4}x\right)=9\qquad\text{subtract 10 from both sides}\\\\-2\log_9\left(\dfrac{1}{4}x\right)=-1\qquad\text{divide both sides by (-2)}\\\\\log_9\left(\dfrac{1}{4}x\right)=\dfrac{1}{2}\iff\dfrac{1}{4}x=9^\frac{1}{2}\\\\\dfrac{1}{4}x=\sqrt9\\\\\dfrac{1}{4}x=3\qquad\text{multiply both sides by 4}\\\\x=12\in D$

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