Question

If $3(\log 5-\log 3)-(\log 5-2\log 6)=2-\log x,$ find $x$.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is B $3$

$3(\log 5-\log 3)-(\log 5-2\log 6)=2-\log x$

$3\log \left(\frac{5}{3}\right)-\log \left(\frac{5}{6^2}\right)=2-\log x$

$\log {\left(\frac{5}{3}\right)}^3-\log \left(\frac{5}{36}\right)=\log 100-\log x$

$\log \left(\frac{125}{27}\right)-\log \left(\frac{5}{36}\right)+\log x=\log 100$

$\log \left(\frac{125\times 36}{27\times 5}\right)+\log x=\log 100$

$\log \left(\frac{100}{3}\right)+\log x=\log 100$

$\log \left(\frac{100x}{3}\right)=\log 100$

$\left(\frac{100x}{3}\right)=100$

$\Rightarrow x=3$