Question

# If $$\displaystyle \log_{10}x=y$$, then the value of $$\displaystyle \log _{1000}x^{2}$$ in terms of $$y$$ is

A
y3
B
y3
C
2y3
D
2y3

Solution

## The correct option is C $$\dfrac{2y}3$$$$\log _{ 10 } x=y$$$$\Rightarrow \dfrac { 2\log { x } }{ 3\log { 10 } } =\dfrac { 2y }{ 3 }\left[\because \log_ba=\dfrac{\log a}{\log a} \right]$$$$\Rightarrow \dfrac { \log { x^2 } }{ \log { 10^3 } }[\because x\log a=\log a^x] =\dfrac { 2y }{ 3 }$$$$\Rightarrow \log _{ 1000 }{ { x }^{ 2 } } =\dfrac { 2y }{ 3 }$$Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More