Решете log_{4}(3a+4b)=log_{2}sqrt{ab}

$$\log _ { 4 } ( 3 a + 4 b ) = \log _ { 2 } \sqrt { a b }$$

Решаване за a (complex solution)

$$a=\frac{4b}{b-3}$$

$$b\neq 0\text{ and }b\neq 3\text{ and }Im(\ln(4b+\frac{12b}{b-3}))-2Im(\ln(\sqrt{\frac{b^{2}}{b-3}}))=0$$

Решаване за b (complex solution)

$$b=\frac{3a}{a-4}$$

$$a\neq 0\text{ and }a\neq 4\text{ and }Im(\ln(3a+\frac{12a}{a-4}))-2Im(\ln(\sqrt{\frac{a^{2}}{a-4}}))=0$$

Решаване за a

$$a=\frac{4b}{b-3}$$

$$b>3$$

Решаване за b

$$b=\frac{3a}{a-4}$$

$$a>4$$