Question

Показательные уравнение и неравенства.
Решите уравнения.

Answer 1

$1)2^{x}=1\\2^{x}= 2^{o}\\x=0\\\\2)\pi^ {x}=1\\\pi ^{x}= \pi ^{o}\\ x=0$

$3)(\frac{1}{\sqrt{2}}) ^{x^{3}-9x} =1\\\\(\frac{1}{\sqrt{2}}) ^{x^{3} -9x}=( \frac{1}{\sqrt{2}}) ^{o}\\x^{3}-9x=0\\x(x^{2} -9)=0\\x(x-3)(x+3)=0\\x_{1} =0;x_{2}=-3; x_{3}=3$

$4)\sqrt{3^{x}}=9\\\\ 3^{x}=81\\\\ 3^{x}= 3^{4}\\ x=4$

$5)(\frac{2}{5}) ^{x}=( \frac{5}{2}) ^{4}\\\\(\frac{2}{5}) ^{x}=( \frac{2}{5}) ^{-4}\\\\x=-4$

$6)(\frac{2}{3}) ^{x}*( \frac{9}{8}) ^{x}= \frac{27}{64}\\\\(\frac{2}{3}* \frac{9}{8}) ^{x}= \frac{27}{64}\\\\(\frac{3}{4}) ^{x}=( \frac{3}{4}) ^{3}\\ x=3$