Question

expand log ( m^3 n^4/ p^2 ) using the laws of lagorithm​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:\log\:\left(\:\dfrac{m^3\:n^4}{p^2}\:\right)\:=\:3\:\log\:(\:m\:)\:+\:4\:\log\:(\:n\:)\:-\:2\:\log\:(\:p\:)\:}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\log\:\left(\:\dfrac{m^3\:n^4}{p^2}\:\right)}$

We have to expand the given expression.

Now,

$\displaystyle{\sf\:\log\:\left(\:\dfrac{m^3\:n^4}{p^2}\:\right)}$

We know that,

$\displaystyle{\pink{\sf\:\log_b\:\left(\:\dfrac{x}{y}\:\right)\:=\:\log_b\:(\:x\:)\:-\:\log_b\:(\:y\:)}}$

$\displaystyle{\implies\sf\:\log\:(\:m^3\:n^4\:)\:-\:\log\:(\:p^2\:)}$

We know that,

$\displaystyle{\pink{\sf\:\log_b\:(\:xy\:)\:=\:\log_b\:(\:x\:)\:+\:\log_b\:(\:y\:)}}$

$\displaystyle{\implies\sf\:\log\:(\:m^3\:)\:+\:\log\:(\:n^4\:)\:-\:\log\:(\:p^2\:)}$

We know that,

$\displaystyle{\pink{\sf\:\log_b\:(\:a^k\:)\:=\:k\:\log_b\:(\:a\:)}}$

$\displaystyle{\implies\sf\:3\:\log\:(\:m\:)\:+\:4\:\log\:(\:n\:)\:-\:2\:\log\:(\:p\:)}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:\log\:\left(\:\dfrac{m^3\:n^4}{p^2}\:\right)\:=\:3\:\log\:(\:m\:)\:+\:4\:\log\:(\:n\:)\:-\:2\:\log\:(\:p\:)\:}}}}$

Answer 2

Step-by-step explanation:

Answer:

$\displaystyle{\boxed{\red{\sf\:\log\:\left(\:\dfrac{m^3\:n^4}{p^2}\:\right)\:=\:3\:\log\:(\:m\:)\:+\:4\:\log\:(\:n\:)\:-\:2\:\log\:(\:p\:)\:}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\log\:\left(\:\dfrac{m^3\:n^4}{p^2}\:\right)}$

We have to expand the given expression.

Now,

$\displaystyle{\sf\:\log\:\left(\:\dfrac{m^3\:n^4}{p^2}\:\right)}$

We know that,

$\displaystyle{\pink{\sf\:\log_b\:\left(\:\dfrac{x}{y}\:\right)\:=\:\log_b\:(\:x\:)\:-\:\log_b\:(\:y\:)}}$

$\displaystyle{\implies\sf\:\log\:(\:m^3\:n^4\:)\:-\:\log\:(\:p^2\:)}$

We know that,

$\displaystyle{\pink{\sf\:\log_b\:(\:xy\:)\:=\:\log_b\:(\:x\:)\:+\:\log_b\:(\:y\:)}}$

$\displaystyle{\implies\sf\:\log\:(\:m^3\:)\:+\:\log\:(\:n^4\:)\:-\:\log\:(\:p^2\:)}$

We know that,

$\displaystyle{\pink{\sf\:\log_b\:(\:a^k\:)\:=\:k\:\log_b\:(\:a\:)}}$

$\displaystyle{\implies\sf\:3\:\log\:(\:m\:)\:+\:4\:\log\:(\:n\:)\:-\:2\:\log\:(\:p\:)}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:\log\:\left(\:\dfrac{m^3\:n^4}{p^2}\:\right)\:=\:3\:\log\:(\:m\:)\:+\:4\:\log\:(\:n\:)\:-\:2\:\log\:(\:p\:)\:}}}}$

muskan Joshi