Question

log_{2}(2-x)-2=log_{2} (x+8)

Answer 1

\[\log_{2}(2-x)-2=\log_{2} (x+8)\]

Answer 2

step by step please

Answer 3

\[\large \log_{2}(2-x)-2=\log_{2} (x+8)\]



\[\large \log_{2}(2-x)-\log_{2}(4)=\log_{2} (x+8)\]



\[\large \log_{2}\left(\frac{2-x}{4}\right)=\log_{2} (x+8)\]



\[\large \frac{2-x}{4}=x+8\]



\[\large 2-x=4(x+8)\]



\[\large 2-x=4x+32\]



\[\large 2-32=4x+x\]



\[\large -30=5x\]



\[\large \frac{-30}{5}=x\]



\[\large -6=x\]



\[\large x=-6\]

Answer 4

notes: I converted 2 to \[\log_2(4)\] because I wanted everything inside a log with base 2

Answer 5

so 2 = \[\log_{2}4 \] ?

Answer 6

\[\large \log_{2}(4)=\log_{2}(2^2)=2\log_{2}(2)=2(1)=2\]
So \[\large \log_{2}(4)=2\]

Answer 7

thank you again!