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^{(\frac{1}{2})}}{2\cdot5})$$\log _a(\frac{3^{(\frac{1}{2})}}{2\cdot5})=\log _a3^{(\frac{1}{2})}-\log _a(2\cdot5)$$\log _a3^{(\frac{1}{2})}-\log _a(2\cdot5)=\frac{1}{2}\log _a3-(\log _a2+\log _a5)$$\frac{1}{2}\log _a3-(\log _a2+\log _a5)=\frac{1}{2}\log _a3-\log _a2-\log _a5$

substitute given values

$\frac{1}{2}\log _a3-\log _a2-\log _a5=\frac{1}{2}\cdot0.6131-0.3869-0.8982$$\frac{1}{2}\cdot0.6131-0.3869-0.8982=-0.9786$

The answer is -0.9786