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!!