Question

Solve the equation:

\[log_4(x)+log_7(x)=1\]

Answer 1

I have no idea what to do...

Answer 2

Hint:

\[\Large \log_{b}(x) = \frac{\log_{10}(x)}{\log_{10}(b)}\]

or

\[\Large \log_{b}(x) = \frac{\ln(x)}{\ln(b)}\]


The second equation may be easier to work with


So this means that


\[\Large log_4(x)+log_7(x)=1\]


is the same as


\[\Large \frac{\ln(x)}{\ln(4)} + \frac{\ln(x)}{\ln(7)} = 1\]

Answer 3

We did not learn the base change formula in class... so I need someone to help me out with an example first because I have no clue how to do these things... :'(

Answer 4

\[\frac{\log_{10}x}{\log_{10}4}+\frac{\log_{10}x}{\log_{10}7}=\log_{10}10 \]