Hello users,

I am trying to help my dad in working out a maths solution that he simply cannot understand. Maths had never been my strong subject but my dad is trying to reconnect with his past education questions done many years ago. I would be grateful if someone could provide a working solution as to how to calculate this question.

$\log_{16}(x y) = \log_{16}(x) + \log_{16}(y)=$

$\dfrac {\log_{4}(x)}{\log_4(16)} + \dfrac {\log_{4}(y)}{\log_4(16)}=$

$\dfrac {\log_4(x)}{\log_4(4^2)}+\dfrac {\log_4(y)}{\log_4(4^2)}=$

$\dfrac {\log_4(x)}{2}+\dfrac {\log_4(y)}{2}$

Can you use these logarithm laws: \displaystyle \begin{align*} \log_{a}{ \left( n^p \right) } = p\log_a{(n)} \end{align*} and \displaystyle \begin{align*} \log_{a}{\left( m\,n \right) } = \log_a{(m)} + \log_{a}{(n)} \end{align*} to simplify the right hand side to a single logarithm?

Thank you. But being an idiot I forgot to say using the above formula please solve the similtanious equations

Log16(xy) =3 1/2 (3 and half)

(log 4x)
-------- = -8
(log4y)

But being an idiot I forgot to say using the above formula please solve the similtanious equations

Log16(xy) =3 1/2 (3 and half)

(log 4x)
-------- = -8
(log4y)[/QUOTE]

Thank you. But being an idiot I forgot to say using the above formula please solve the similtanious equations

Log16(xy) =3 1/2 (3 and half)

(log 4x)
-------- = -8
(log4y)
You need to at least show some effort. What have you tried so far?

We have done the following we have done the first part by channing the bae from 16 to 4. Now to do the 2nd part we know from the first part that half of log x to the base 4 + 1/2 of log of y to the base 4 =3.5 (3 and half).

From the 2nd part of the equation is log of x to the base 4 - log of y to the base 4 = -8. This is gained by using the 2nd logarithm law. That is as far as we got, if my dad tries to solve these equations we are unable to do so due to some complications.

We don't know which law and how to use it to get the answer.

He done this type of questions in 1956 and his memory is not as strong as it used to be. It is more for nostalgic reasons he would like to reconnect to his maths.

We have done the following we have done the first part by channing the bae from 16 to 4. Now to do the 2nd part we know from the first part that half of log x to the base 4 + 1/2 of log of y to the base 4 =3.5 (3 and half).

From the 2nd part of the equation is log of x to the base 4 - log of y to the base 4 = -8. This is gained by using the 2nd logarithm law. That is as far as we got, if my dad tries to solve these equations we are unable to do so due to some complications.

We don't know which law and how to use it to get the answer.

He done this type of questions in 1956 and his memory is not as strong as it used to be. It is more for nostalgic reasons he would like to reconnect to his maths.