Question

Bài 1: Tìm n \(\in\) Z biết:

\(e)3^{-1}.3^n+6.3^{n-1}=7.3^6\)

\(g)3^4< \dfrac{1}{9}.27^n< 3^{10}\)

\(h)25< 5^n:5< 625\)

Bài 2: Tìm x biết:

\(\dfrac{2.\left(\dfrac{-1}{2}\right).\left(\dfrac{2}{3}\right)^2-3.\left(\dfrac{-1}{2}\right)^2.\dfrac{2}{3}+1}{3.\left(\dfrac{-1}{2}\right)-\dfrac{2}{3}}\)

Help me !!!!!!!!!!!!! giúp mk vs các bn giỏi toán

Answer 1

e) 3^-1.3ⁿ+6.3^n-1=7.3⁶

<=>3^n-1+6.3^n-1=7.3⁶

<=>3^n-1.7=7.3⁶

=>3^n-1=3⁶=>n-1=6=>n=7

Answer 2

\(3^4< \dfrac{1}{9}.27^n< 3^{10}< =>3^6.\dfrac{1}{9}< 3^{3n}.\dfrac{1}{9}< 3^{12}.\dfrac{1}{9}\)

\(< =>3^6< 3^{3n}< 3^{12}=>6< 3n< 12\)

\(< =>2< n< 4=>n=3\)

Answer 3

h) 25<5ⁿ:5<625

<=>5²<5^n-1<5⁴=>2<n-1<4=>3<n<5=>n=4

Answer 4

Bài 1:

e)3^-1.3ⁿ+6.3^n-1=7.3⁶

\(\dfrac{1}{3}.3^n\)+6.3^n-1=7.3⁶

1.3ⁿ+6.3^n-1=7.3⁶

3ⁿ.(1+6)=7.3⁶

3ⁿ.7=7.3⁶

\(\Rightarrow\)n=6

Những bài còn lại bạn tự làm nhé!!!

Answer 5

\(\dfrac{2.\left(\dfrac{-1}{2}\right).\left(\dfrac{2}{3}\right)^2-3.\left(\dfrac{-1}{2}\right)^2.\dfrac{2}{3}+1}{3.\left(\dfrac{-1}{2}\right)-\dfrac{2}{3}}\)

\(=\dfrac{-1.\left(\dfrac{2}{3}\right)^2-2.\left(\dfrac{-1}{2}\right)^2+1}{\dfrac{-3}{2}-\dfrac{2}{3}}\)

\(=\dfrac{-\dfrac{4}{9}-\dfrac{1}{2}+1}{\dfrac{-13}{6}}=\dfrac{1}{18}.\dfrac{6}{-13}=\dfrac{1}{-39}=\dfrac{-1}{39}\)