Question

[dương trà my]

tìm x En biết

1)2^x-15=17

2)(7x-11)³=2⁵.5²+200

3)3^x+25=26.2²+2.3⁰

4)49.7^x=2041

5)3^x=243

Answer 1

[Nam Nguyễn]

Giải:

\(a,2^x-15=17.\)

\(2^x=17+15.\)

\(2^x=32.\)

\(2^x=2^5.\)

\(\Rightarrow x=5\in N.\)

Vậy \(x=5.\)

\(b,\left(7x-11\right)^3=2^5.5^2+200.\)

\(\left(7x-11\right)^3=32.25+200.\)

\(\left(7x-11\right)^3=800+200.\)

\(\left(7x-11\right)^3=1000.\)

\(\left(7x-11\right)^3=10^3.\)

\(\Rightarrow7x-11=10.\)

\(\Rightarrow7x=10+11=21.\)

\(\Rightarrow x=21:7=3\in N.\)

Vậy \(x=3.\)

\(c,3^x+25=26.2^2+2.3^0.\)

\(3^x+25=26.2^2+2.1.\)

\(3^x+25=2\left(26.2+1\right).\)

\(3^x+25=2.53.\)

\(3^x+25=106.\)

\(3^x=106-25.\)

\(3^x=81.\)

\(3^x=3^4\Rightarrow x=4\in N.\)

Vậy \(x=4.\)

\(d,49.7^x=2041.\)(đề này sai).

Sửa đề:

\(49.7^x=2401.\)

\(7^x=2401:49.\)

\(7^x=49.\)

\(7^x=7^2\Rightarrow x=2\in N.\)

Vậy \(x=2.\)

\(e,3^x=243.\)

\(3^x=3^5\Rightarrow x=5\in N.\)

Vậy \(x=5.\)

~ Học tốt!!! ~

Answer 2

[Đức Hiếu]

a, \(2^x-15=17\)

\(\Rightarrow2^x=32\Rightarrow2^x=2^5\)

Vì \(2\ne-1;2\ne0;2\ne1\) nên \(x=5\)

Vậy....

b, \(\left(7x-11\right)^3=2^5.5^2+200\)

\(\Rightarrow\left(7x-11\right)^3=32.25+200\)

\(\Rightarrow\left(7x-11\right)^3=1000=10^3\)

\(\Rightarrow7x-11=10\Rightarrow7x=21\Rightarrow x=3\)

Vậy.....

c, \(3^x+25=26.2^2+2.3^0\)

\(\Rightarrow3^x+25=26.4+2\)

\(\Rightarrow3^x=104+2-25\)

\(\Rightarrow3^x=81=3^4\)

Vì \(3\ne-1;3\ne0;3\ne1\) nên x=4

Vậy.....

d,Sửa đề:\(49.7^x=2401\)

\(\Rightarrow7^2.7^x=7^4\Rightarrow7^{2+x}=7^4\)

Vì \(7\ne-1;7\ne0;7\ne1\) nên \(2+x=4\Rightarrow x=2\)

Vậy.....

Câu e làm tương tự! Chúc bạn học tốt!!!