Question

MEDAL!!
Solving logarithm equation

Answer 1

\[\log_{4}(x-4)+\log_{4}(x)=\log_{4}(5)\]
\[\log(a)+\log(b)=\log(ab)\]
\[\log_{4}\left[ (x-4)(x) \right]=\log_{4}(5)\]

now you will do the inverse of base 4 logarithm
that is doing 4 to the power of everything
to get
\[4^{\log_{4}\left[ (x-4)(x) \right]}=4^{\log_{4}(5)}\]

since they are inverses
\[\log_{4}4=1\]
\[\log_{4}4^{x}=x\]

so we get

\[(x-4)(x)=5\]

Answer 2

solve for x

Answer 3

do i distribut the 5??

Answer 4

you would get a quadratic, yes

Answer 5

any questions?

Answer 6

would appreciate medal for best answer if you don't have anything else to ask