Maria wrote the equation log(x/2)+log(20/x^2)=log8. What is the solution to Maria's equation?a. x=3/10b. x=4/5c. x=5/4d. x10/3
Accepted Solution
A:
The solution is x=5/4.
We use the properties of logs to rewrite the equation: [tex]\log[(\frac{x}{2})(\frac{20}{x^2})]=\log8
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\\\log(\frac{20x}{2x^2})=\log8
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\\\log(\frac{10}{x})=\log8[/tex]
Get all of the logs on the same side of the equation y subtracting log 8: [tex]\log(\frac{10}{x})-\log8=\log8 - \log8
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\\\log(\frac{10}{x})-\log8=0[/tex]
Use the properties of logs to rewrite: [tex]\log(\frac{10}{x}\div8)=0
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\\\log(\frac{10}{x}\div\frac{8}{1})=0
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\\\log(\frac{10}{x}\times\frac{1}{8})=0
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\\\log(\frac{10}{8x})=0[/tex]