Question

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.

Answer 1

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