Answer
a) $\dfrac{1}{2}$ b) $\log_{25}[\dfrac{x(x^2-1)^5}{5(x+1)}]$
Work Step by Step
a) Since, $\log_{25} {5}=\log _{25}(25)^{1/2}=\dfrac{1}{2}$
b) Now
$\log_{25} x+5\log_{25}(x^2-1)-\log_{25}(x+1)-\dfrac{1}{2}=\log_{25} x+5\log_{25}(x^2-1)-\log_{25}(x+1)-\log_{25} {5}$ [From part (a), we have $\log_{25} {5}=\dfrac{1}{2}$]
or, $=[\log_{25}x+\log_{25}(x^2-1)^5]-[\log_{25}(x+1)+\log_{25}5]$
or, $=\log_{25}[x(x^2-1)^5]-\log_{25}[5(x+1)]$
or, $=\log_{25}[\dfrac{x(x^2-1)^5}{5(x+1)}]$
Hence, a) $\dfrac{1}{2}$ b) $\log_{25}[\dfrac{x(x^2-1)^5}{5(x+1)}]$
