Question

Solve the logarithmic equation below.

Answer 1

\[2 \log _{4}(5-x) - \log _{4}2=\log _{4}50\]
That is the problem.

Answer 2

@satellite73 @jdoe0001 @cwrw238

Answer 3

I know \[\log_{4}2=.4\]

Answer 4

actually .5 but no matter

Answer 5

And
\[\log_{4}50=\frac{ \log 50 }{ \log 4 }\]

Answer 6

Oops that was a typo..

Answer 7

you can write
\[\log_4((5-x)^2) -.5=\log_4(50)\] if you like

Answer 8

Ok.

Answer 9

but really lets just leave the \[\log_4(2)\] alone and add it to the right
\[\log_4((5-x)^2)=\log_4(50)+\log_4(2)\]

Answer 10

or \(\bf {\color{brown}{ 2}} \log _{4}(5-x) - \log _{4}2
\\ \quad \\
\log _{4}(5-x)^{\color{brown}{ 2}} - \log _{4}2=\log _{4}50\implies log_4\left(\cfrac{(5-x)^2}{2}\right)=log _{4}50\)

and you could pretty much see the equation there

Answer 11

that tells you
\[\log_4((5-x)^2)=\log_4(100)\] making
\[(x-5)^2=100\] and that is real easy to solve

Answer 12

It was that easy.. I feel so dumb lol

Answer 13

you can just about solve that one in your head
either
\[5-x=10\\
x=-5\] or
\[5-x=-10\\
x=15\]

Answer 14

check that the negative solution probably doesn't work in the original equation so toss that one out

Answer 15

Thank you so much @satellite73 @jdoe0001 :)

Answer 16

yw

Answer 17

Actually -5 was the answer not 15 but thanks.