What is 2log_{c}(z+3)+log_{c}(3z+4) ?

The solution to 2log_{c}(z+3)+log_{c}(3z+4) is log_{c}((z+3)^2(3z+4))

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simplify 2log_{c}(z+3)+log_{c}(3z+4)

simplify

2 lo g_{c} (z + 3) + lo g_{c} (3 z + 4)

lo g_{c} ((z + 3)^{2} (3 z + 4))

Solution steps

2 lo g_{c} (z + 3) + lo g_{c} (3 z + 4)

Apply log rule:

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

2 lo g_{c} (z + 3) = lo g_{c} ((z + 3)^{2})

= lo g_{c} ((z + 3)^{2}) + lo g_{c} (3 z + 4)

Apply log rule:

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

lo g_{c} ((z + 3)^{2}) + lo g_{c} (3 z + 4) = lo g_{c} ((z + 3)^{2} (3 z + 4))

= lo g_{c} ((z + 3)^{2} (3 z + 4))

ln (e^{4 x} (\frac{x ^{5} - 8 x + 6}{cos ( x )}))

\frac{1}{4} [3 ln (x + 7) - ln (x) - ln (x^{2} - 25)]

2 ln (x + 2) - ln (x)

lo g_{3} (9 s)

What is 2log_{c}(z+3)+log_{c}(3z+4) ?
The solution to 2log_{c}(z+3)+log_{c}(3z+4) is log_{c}((z+3)^2(3z+4))