What is clog_{a}(x)+2log_{a}(y)-4log_{a}(x) ?

The solution to clog_{a}(x)+2log_{a}(y)-4log_{a}(x) is clog_{a}(x)+log_{a}((y^2)/(x^4))

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simplify clog_{a}(x)+2log_{a}(y)-4log_{a}(x)

simplify

c lo g_{a} (x) + 2 lo g_{a} (y) - 4 lo g_{a} (x)

c lo g_{a} (x) + lo g_{a} (\frac{y ^{2}}{x ^{4}})

Solution steps

c lo g_{a} (x) + 2 lo g_{a} (y) - 4 lo g_{a} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{a} (y) = lo g_{a} (y^{2})

= c lo g_{a} (x) + lo g_{a} (y^{2}) - 4 lo g_{a} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{a} (x) = lo g_{a} (x^{4})

= c lo g_{a} (x) + lo g_{a} (y^{2}) - lo g_{a} (x^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{a} (y^{2}) - lo g_{a} (x^{4}) = lo g_{a} (\frac{y ^{2}}{x ^{4}})

= c lo g_{a} (x) + lo g_{a} (\frac{y ^{2}}{x ^{4}})

lo g_{10} (5 \frac{6}{x ^{7}})

lo g_{5} (\frac{25 b ^{5} y ^{2} - 1}{y ( x + 1 ) ^{2}})

ln (\frac{1}{e ^{8}}) + ln (8) e^{3}

ln (x^{6}) - 2 ln (x^{3})

2 ln (3) + ln (4)

What is clog_{a}(x)+2log_{a}(y)-4log_{a}(x) ?
The solution to clog_{a}(x)+2log_{a}(y)-4log_{a}(x) is clog_{a}(x)+log_{a}((y^2)/(x^4))