Question

Hi can somebody help me please:

4 log x = log 4 x

im a bit stuck on this one. :(

Answer 1

hi,
Is it something like this ?\[4logx = \log4x\]
and u r trying to solve it for x ?

Answer 2

yes

Answer 3

Hi,
this is a basic rule u need to solve this question
\[\log a + \log b = \log (ab)\]
So...
apply it to the log4x and rewrite it as this....
\[\log4x = \log4 + logx\]

now ur question is modified to this...
\[4logx = logx + \log 4\]\[4logx - \log x = \log 4\]\[3logx = \log4 \]\[logx = \frac{ \log4 }{3}\]

Now let's take
\[logx = \frac{ \log4 }{3 } = y\]
then
\[\log x = y\]
\[10^{y} = x\ ----(1) \]

also
\[\frac{ \log4 }{3 } = y\]\[\log4 = 3y\]\[10^{3y} = 4\]\[(10^{y})^{3} =4\]\[10^{y} = \sqrt[3]{4} ----(2)\]


hence the left side of (1) = (2) ---> The right hand side also should equal
which mean
\[x = \sqrt[3]{4}\]

Hope this will hep ya!!!

Answer 4

that really helps thanks so much!

Answer 5

u r welcome!!