Explain why domain restrictions for inverse trigonometric functions are necessary
1 answer:
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The solution is x=5/4.
We use the properties of logs to rewrite the equation:
![\log[(\frac{x}{2})(\frac{20}{x^2})]=\log8 \\ \\\log(\frac{20x}{2x^2})=\log8 \\ \\\log(\frac{10}{x})=\log8](https://tex.z-dn.net/?f=%5Clog%5B%28%5Cfrac%7Bx%7D%7B2%7D%29%28%5Cfrac%7B20%7D%7Bx%5E2%7D%29%5D%3D%5Clog8%0A%5C%5C%0A%5C%5C%5Clog%28%5Cfrac%7B20x%7D%7B2x%5E2%7D%29%3D%5Clog8%0A%5C%5C%0A%5C%5C%5Clog%28%5Cfrac%7B10%7D%7Bx%7D%29%3D%5Clog8)
Get all of the logs on the same side of the equation y subtracting log 8:
Use the properties of logs to rewrite:
Exponentiate:
Multiply both sides by 8x:
1*8x = (10/8x)*8x
8x=10
Divide both sides by 8:
8x/8 = 10/8
x = 10/8 = 5/4
We use the properties of logs to rewrite the equation:
Get all of the logs on the same side of the equation y subtracting log 8:
Use the properties of logs to rewrite:
Exponentiate:
Multiply both sides by 8x:
1*8x = (10/8x)*8x
8x=10
Divide both sides by 8:
8x/8 = 10/8
x = 10/8 = 5/4