Question

2log base b of x = 3 log base b of (1-a) + 2 log base b of (1+a) - log base b of (1/a -a)^2

Answer 1

\[2\log_b{x}=3\log_{b}(1-a)+2\log_{b}(1+a)-\log_{b}(\frac{1}{a}-a)^2\]
\[2\log_{b}x=\log_{b}(1-a)^3+\log_{b}(1+a)^2-\log_{b}(\frac{1-a^2}{a})^2\]
\[2\log_{b}x=\log_{b}\frac{(1-a)^3(1+a)^2}{(\frac{1-a^2}{a})^2}\]
\[2\log_{b}x=\log_{b}(\frac{a^2(1-a)^3(1+a)^2}{(1-a^2)^2})\]
\[2\log_{b}x=\log_{b}(\frac{a^2(1-a^2)^2(1-a)}{(1-a^2)^2})\]
\[2\log_{b}x=\log_{b}[a^2(1-a)]\]
\[\log_{b}x=\frac{\log_{b}[a^2(1-a)]}{2}\]
\[\large b^\frac{\log_{b}[a^2(1-a)]}{2}=x\]
\[x=a^2(1-a)\]

Answer 2

think i messed up on the very last line

Answer 3

\[\large b^{{\log_{b}[a^2(1-a)]}^{\frac{1}{2}}}=x\]
\[x=\sqrt{[a^2(1-a)]}\]

Answer 4

yea...that was a lot of work...not gonna do it again...please make sure you post the question right