Question

What is the value of $2\log \left(\frac{5}{8}\right)+\log \left(\frac{128}{125}\right)+\log \left(\frac{5}{2}\right)$?

• A. $0$
• B. $1$
• C. $2$
• D. $5$

Answer 1

The correct option is A $0$

$2log\left(\frac{5}{8}\right)+log\left(\frac{128}{125}\right)+log\left(\frac{5}{2}\right)$

$\Rightarrow 2[log5-log{2}^3]+[log{2}^7-log{5}^3]+[log5-log2]$

$\Rightarrow 2log5-6log2+7log2+3log5+log5-log2$

$=0$