Помогитн решить тема логарифмы

Question

Математика

Doomshaper

6 год назад

Помогитн решить тема логарифмы

ОТВЕТЫ

Кайсаров

Aug 8, 2019

1. $2^x=2^4amp;#10; \\ x=4$
2. $2^{2x}=2^9amp;#10; \\ 2x=9amp;#10; \\ x=4.5$
3. $2^{-x}=2^4amp;#10; \\ -x=4amp;#10; \\ x=-4$
4. $3^{2x-1}=3^4amp;#10; \\ 2x-1=4amp;#10; \\ x=2.5$
5. $5^{ \frac{x}{2} }=5^{ \frac{2}{3} }amp;#10; \\ \frac{x}{2} = \frac{2}{3}amp;#10; \\ x= \frac{2*2}3}= \frac{4}{3}$
6. $3^{2x-1}=3^0amp;#10; \\ 2x-1=0amp;#10; \\ x=0.5$
7. $(2*5)^x= 10^-2*10^{5x-5}amp;#10; \\ 10^x=10^{-2+5x-5}amp;#10; \\ 10^x=10^{5x-7}amp;#10; \\ x=5x-7amp;#10; \\ -4x=-7amp;#10; \\ x= \frac{7}{4} =1.75amp;#10;$
8. $( \frac{2}{3} )^{2x}= (\frac{3}{2} )^8amp;#10; \\ ( \frac{3}{2})^{-2x}=( \frac{3}{2} )^8amp;#10; \\ -2x=8amp;#10; \\ x=-4$
9. $2^{2x} +2^x*2^1=8amp;#10; \\ 2^x=tamp;#10; \\ t^2+2t-8=0amp;#10; \\ D=4-4*1*(-8)=4+32=36=6^{2} amp;#10; \\ x1= \frac{-2+6}{2} =2 \\ x2= \frac{-2-6}{2}=-4amp;#10; \\ 2^x=2 \\ x=1amp;#10; \\ 2^x=-4$
10. $3^2*3^x+3^x*3^-1=28amp;#10; \\ 3^x(9+ \frac{1}{3})=28 \\ 3^x* \frac{28}{3} =28 \\ 3^x= \frac{28}{ \frac{28}{3} } \\ 3^x=3^1 \\ x=1$
11. $2^x*2+3*2^x*2^{-1}-5*2^x+6=0 \\ 2^x(2+1.5-5)=-6 \\ 2^x*(-1.5)=-6 \\ 2^x=-6/(-1.5) \\ 2^x=4 \\ 2^x=2^2 \\ x=2$

123