Question

MEDAL!!
log
im stuck

Answer 1

yup proceed ...@clamin

Answer 2

u will get a quadratic equation in "x"
solve it to get "x"

Answer 3

\(\log_{2}4 = \log_{2}2^2 = 2\)

Answer 4

now just solve^^

Answer 5

@M4thM1nd where did you get 4 from?

Answer 6

\(\large {
log_2(9x+5)-log_2(x^2-1)=2\implies log_2\left( \cfrac{9x+5}{x^2-1} \right)=2
\\ \quad \\
\textit{log cancellation of }{\color{brown}{ a}}^{log_{\color{brown}{ a}}x}=x\qquad thus
\\ \quad \\
\Large {\color{brown}{ 2}}^{ log_{\color{brown}{ 2}}\left( \frac{9x+5}{x^2-1} \right)}={\color{brown}{ 2}}^2\implies ?
}\)

Answer 7

He has \(\log_{2}(\frac{9x+5}{x^2-1}) = 2 = \log_{2}4\), so...
\(\frac{9x+5}{x^2-1} = 4\)

Answer 8

anyhow..,. as you can see
using that log cancellation rule
where we give a base to both sides of "2", that is, the log base

that drops off our term down

thus \(\Large {
{\color{brown}{ 2}}^{ log_{\color{brown}{ 2}}\left( \frac{9x+5}{x^2-1} \right)}={\color{brown}{ 2}}^2\implies \cfrac{9x+5}{x^2-1}=4
}\)

Answer 9

thats all?

Answer 10

can i cancel if theres the same variable or number inside the parenthesis??