Question

Логорифмы. Помогите -50баллов.

Answer 1

$1)\; \; \; log_{3\sqrt[4]3}(27\cdot \sqrt3)+log_{4\sqrt{32}}(8\cdot \sqrt2)=\\\\=log_{3^{5/4}}\, 3^{\frac{7}{2}}+log_{2^{9/2}}\, 2^{\frac{7}{2}}= \frac{4}{5}\cdot \frac{7}{2} \cdot log_33+ \frac{2}{9}\cdot \frac{7}{2} \cdot log_22=\\\\= \frac{14}{5} +\frac{7}{9} =\frac{161}{45}= 3\frac{26}{45}$

$2)\; \; \; log_5(log_{10}\sqrt{x^2+19})=0\; ,\; \; \; ODZ:\; \; x\in R\\\\lg\sqrt{x^2+19}=5^0\\\\lg\sqrt{x^2+19}=1\\\\\sqrt{x^2+19}=10^1\\\\x^2+19=100\\\\x^2=81\\\\x=-9\; \; ili\; \; x=9$

$P.S.\; \; \; log_{10}x=lgx\; ,\; \; log_{e}x=lnx$