Condense the following logs into a single log:[tex]8log_{g} x+5log_{g} y[/tex][tex]8log_{5} x+\frac{3}{4} log_{5} y-5log_{5} z[/tex]

QUESTION 1The given logarithm is[tex]8\log_g(x)+5\log_g(y)[/tex]We apply the power rule of logarithms; [tex]n\log_a(m)=\log_(m^n)[/tex][tex]=\log_g(x^8)+\log_g(y^5)[/tex]We now apply the product rule of logarithm;[tex]\log_a(m)+\log_a(n)=\log_a(mn)[/tex][tex]=\log_g(x^8y^5)[/tex]QUESTION 2The given logarithm is [tex]8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)[/tex]We apply the power rule of logarithm to get;[tex]=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)[/tex]We apply the product to obtain;[tex]=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)[/tex]We apply the quotient rule; [tex]\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )[/tex][tex]=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})[/tex][tex]=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})[/tex]