Question

If $a=b^2=c^4=d^8=e^{16}\ne 1$, where $b,c,d,e>0,$ then the value of ${\log }_{cde}abc$ is

• A. equal to zero
• B. less than $1$
• C. greater than $1$
• D. greater than $4$

Answer 1

The correct option is C greater than $1$

${\log }_{cde}abc$
$={\log }_{(e^4\cdot e^2\cdot e)}(e^{16}\cdot e^8\cdot e^4)$
$={\log }_{e^7}{e}^{28}=\frac{28}{7}=4$