log x- log (x-2)= 4
both logs have a base of 2
find x, show steps

Question

log x- log (x-2)= 4
both logs have a base of 2
find x, show steps

anonymous · Answer

the answer is 32/15 but i keep getting no solution

misty1212 · Answer

$$\log_2\left(\frac{x}{x-2}\right)=4$$ is how you want to begin

solomonzelman · Answer

$\large\color{teal}{ \log_2x-\log_2(x-2)=4  }$

$\large\color{teal}{ \log_2x=4+\log_2(x-2)  }$

$\large\color{teal}{ \log_2x=4\times \log_22+\log_2(x-2)  }$

$\large\color{teal}{ \log_2x= \log_22^4+\log_2(x-2)  }$   continue....

misty1212 · Answer

then write is in equivalent exponential form

misty1212 · Answer

$$\frac{x}{x-2}=2^4$$ is the exponential form

misty1212 · Answer

or better yet 
$$\frac{x}{x-2}=16$$

misty1212 · Answer

solve that for $x$

misty1212 · Answer

you good with that ? that is how you are going to get the $\frac{32}{15}$ that you know is the answer

anonymous · Answer

yeah, thanks