Question

2log base 4x-log base 4(x+5)=2

Answer 1

\[2log_4(x)-log_4(x+5) = 2?\]

Answer 2

Yes

Answer 3

\[2log_4(x)-log_4(x+5) = log_4(x^2) - log_4(x+5) = \]

Answer 4

do you get this step?

Answer 5

Yes thx

Answer 6

\[log(a)-log(b) = log(\frac{a}{b})\]

Answer 7

so
\[log(x^2) - log(x+5)= log(\frac{x^2}{x+5})\]
so
\[log_4(\frac{x^2}{x+5})=2\]
this means
\[4^2 = \frac{x^2}{x+5}\]
so
\[16(x+5) = x^2 \rightarrow x^2-16x-80=0\]
can you solve
\[x^2-16x-80=0?\]

Answer 8

(x-20)(x+4)=0
x=20 and x=-4
but
\[log_4(x) \]
is not defined for x<= 0 so, we take x=20 to be the solution

Answer 9

Thanks!