Solve the equation:

$$log_4(x)+log_7(x)=1$$

Question

Solve the equation:

$$log_4(x)+log_7(x)=1$$

anonymous · Answer

I have no idea what to do...

jim_thompson5910 · Answer

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

anonymous · Answer

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... :'(

mertsj · Answer

$$\frac{\log_{10}x}{\log_{10}4}+\frac{\log_{10}x}{\log_{10}7}=\log_{10}10     $$