Question

The value of \(\text {log}_{0.008}\sqrt{5}+\text{log}_{\sqrt{3}}81-7\) is equal to

• A. \(\frac{1}{3}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{5}{6}\)
• D. \(\frac{7}{6}\)

Answer 1

The Correct Option is C

The given expression can be simplified as follows:

\(log_{0.008}\sqrt{​5}​+log_{\sqrt{3}}\ ​​81−7\)
For \(log⁡_{0.008}\sqrt{5}​:\)

\(=log_{5^{−3}}​(5^{\frac{1}{2}}) \)
\(=log_{⁡5^{−3}}(5^{−\frac{3}{2}}) \)
\(=−\frac{1}{6}\)

For \(log_{\sqrt{⁡3}}\ 81:\)
\(=log⁡_{3^{\frac{1}{2}}}(3^4) \)

\(=log⁡_{3^{\frac{1}{2}}}(3^2) \)
\(=2\)

Putting it all together:
\((−\frac{1}{6})+8−7=−\frac{1}{6}+1=\frac{5}{6}\)

Therefore, the required result is \(\frac{5}{6}.\)