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Mathematics
OpenStudy (anonymous):

Hi can somebody help me please: 4 log x = log 4 x im a bit stuck on this one. :(

OpenStudy (***[isuru]***):

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

OpenStudy (anonymous):

yes

OpenStudy (***[isuru]***):

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!!!

OpenStudy (anonymous):

that really helps thanks so much!

OpenStudy (***[isuru]***):

u r welcome!!

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