Решите уравнения А) 2^х+2 +3*2^х+1+7*2^х=68 Б)log1/5(7x+1/25)=2 B)4lg²x-2=lg*x²

Question

Решите уравнения
А) 2^х+2 +3*2^х+1+7*2^х=68
Б)log1/5(7x+1/25)=2
B)4lg²x-2=lg*x²

Answer 1

0, \\ 7x>-\frac{1}{25}, \\ x>-\frac{1}{175}, \\ 7x+\frac{1}{25}=(\frac{1}{5})^2, \\ 7x=0, x=0; \\ \\ 4\lg^2x-2=\lg x^2, \\ 4\lg^2x -2\lg x -2=0, \\ \lg x = a," alt="2^x+2 +3\cdot2^x+1+7\cdot2^x=68, \\ 10\cdot2^x=65, \\ 2^x=6,5, \\ x=\log_2 6,5; \\ \\ log_{\frac{1}{5}} (7x+\frac{1}{25})=2, \\ 7x+\frac{1}{25}>0, \\ 7x>-\frac{1}{25}, \\ x>-\frac{1}{175}, \\ 7x+\frac{1}{25}=(\frac{1}{5})^2, \\ 7x=0, x=0; \\ \\ 4\lg^2x-2=\lg x^2, \\ 4\lg^2x -2\lg x -2=0, \\ \lg x = a," align="absmiddle" class="latex-formula">