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I don’t have a box for the answer on the picture because the system has an error, but I still need help getting the answer.

I don’t have a box for the answer on the picture because the system has an error, but-example-1
User Janitza
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8.5k points

1 Answer

5 votes

we have the expression


\log _a(\frac{\sqrt[]{3}}{10})

Applying property of exponents and log


\log _a(\frac{\sqrt[]{3}}{10})=\log _a(\frac{3^{((1)/(2))}}{2\cdot5})
\log _a(\frac{3^{((1)/(2))}}{2\cdot5})=\log _a3^{((1)/(2))}-\log _a(2\cdot5)
\log _a3^{((1)/(2))}-\log _a(2\cdot5)=(1)/(2)\log _a3-(\log _a2+\log _a5)
(1)/(2)\log _a3-(\log _a2+\log _a5)=(1)/(2)\log _a3-\log _a2-\log _a5

substitute given values


(1)/(2)\log _a3-\log _a2-\log _a5=(1)/(2)\cdot0.6131-0.3869-0.8982
(1)/(2)\cdot0.6131-0.3869-0.8982=-0.9786

The answer is -0.9786

User Corkey
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