What is (log_{4}(t-4)+log_{4}(2t^2-7t-4))/2 ?

The solution to (log_{4}(t-4)+log_{4}(2t^2-7t-4))/2 is (log_{4}((t-4)(2t^2-7t-4)))/2

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simplify (log_{4}(t-4)+log_{4}(2t^2-7t-4))/2

simplify

\frac{lo g _{4} ( t - 4 ) + lo g _{4} ( 2 t ^{2} - 7 t - 4 )}{2}

\frac{lo g _{4} ( ( t - 4 ) ( 2 t ^{2} - 7 t - 4 ) )}{2}

Solution steps

\frac{lo g _{4} ( t - 4 ) + lo g _{4} ( 2 t ^{2} - 7 t - 4 )}{2}

Apply log rule:

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

lo g_{4} (t - 4) + lo g_{4} (2 t^{2} - 7 t - 4) = lo g_{4} ((t - 4) (2 t^{2} - 7 t - 4))

= \frac{lo g _{4} ( ( t - 4 ) ( 2 t ^{2} - 7 t - 4 ) )}{2}

- 2 lo g_{b} (x) - 3 lo g_{b} (y) + lo g_{b} (z)

lo g_{2} (5 \cdot 6 \cdot 3)

9 lo g_{b} (x) + 3 lo g_{b} (z)

What is (log_{4}(t-4)+log_{4}(2t^2-7t-4))/2 ?
The solution to (log_{4}(t-4)+log_{4}(2t^2-7t-4))/2 is (log_{4}((t-4)(2t^2-7t-4)))/2