What is 2log_{a}(z+6)+log_{a}(3z+5) ?

The solution to 2log_{a}(z+6)+log_{a}(3z+5) is log_{a}((z+6)^2(3z+5))

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simplify 2log_{a}(z+6)+log_{a}(3z+5)

simplify

2 lo g_{a} (z + 6) + lo g_{a} (3 z + 5)

lo g_{a} ((z + 6)^{2} (3 z + 5))

Solution steps

2 lo g_{a} (z + 6) + lo g_{a} (3 z + 5)

Apply log rule:

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

2 lo g_{a} (z + 6) = lo g_{a} ((z + 6)^{2})

= lo g_{a} ((z + 6)^{2}) + lo g_{a} (3 z + 5)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{a} ((z + 6)^{2}) + lo g_{a} (3 z + 5) = lo g_{a} ((z + 6)^{2} (3 z + 5))

= lo g_{a} ((z + 6)^{2} (3 z + 5))

lo g_{5} (\frac{5}{y})

lo g_{10} (a) - lo g_{10} (x) - lo g_{10} (y)

ln (\frac{x}{x - 5}) + ln (\frac{x + 5}{x}) - ln (x^{2} - 25)

lo g_{b} (\frac{x}{yz})

\frac{1}{2} ln (x) + ln (y)

What is 2log_{a}(z+6)+log_{a}(3z+5) ?
The solution to 2log_{a}(z+6)+log_{a}(3z+5) is log_{a}((z+6)^2(3z+5))