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!!! ~
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!!!
1) \(2^x-15=17\)
\(2^x=17+15=32=2^5\)
\(\Rightarrow x=5\)
2) \(\left(7x-11\right)^3=2^5.5^2+200=32.25+200=1000=10^3\)
\(\Rightarrow7x-11=10\)
\(7x=11+10=21\)
\(x=3\)
3) \(3^x+25=26.2^2+2.3^0=26.4+2=106\)
\(3^x=106-25=81=3^4\)
\(\Rightarrow x=4\)
4) \(49.7^x=2041\)
\(7^2.7^x=7^4\)
\(\Rightarrow2+x=4\)
x = 2.
5) \(3^x=243=3^5\)
\(\Rightarrow x=5\)
1) \(2^x-15=17\)
\(\Leftrightarrow2^x=17+15\)
\(\Leftrightarrow2^x=32\)
\(\Leftrightarrow2^x=2^5\)
\(\Leftrightarrow x=5\)
Vậy \(x=5\)
2) \(\left(7x-11\right)^3=2^5\cdot5^2+200\)
\(\Leftrightarrow\left(7x-11\right)^3=32\cdot25+200\)
\(\Leftrightarrow\left(7x-11\right)^3=800+200\)
\(\Leftrightarrow\left(7x-11\right)^3=1000\)
\(\Leftrightarrow\left(7x-11\right)^3=10^3\)
\(\Leftrightarrow7x-11=10\)
\(\Leftrightarrow7x=10+11\)
\(\Leftrightarrow7x=21\)
\(\Leftrightarrow x=3\)
Vậy \(x=3\)
3) \(3^x+25=26\cdot2^2+2\cdot3^0\)
\(\Leftrightarrow3^x+25=26\cdot4+2\cdot1\)
\(\Leftrightarrow3^x+25=106\)
\(\Leftrightarrow3^x=106-25\)
\(\Leftrightarrow3^x=81\)
\(\Leftrightarrow x=4\)
4) \(49\cdot7^x=2401\) (có sửa lại)
\(\Leftrightarrow7^x=49\)
\(\Leftrightarrow7^x=7^2\)
\(\Leftrightarrow x=2\)
Vậy \(x=2\)
5) \(3^x=243\)
\(\Leftrightarrow3^x=3^5\)
\(\Leftrightarrow x=5\)
Vậy \(x=5\)
\(1) \)\(2^x-15=17\Leftrightarrow2^x=15+17=32\Leftrightarrow2^x=32\Leftrightarrow2^x=2^5\Leftrightarrow x=5\)
\(2)\)
\(\left(7x-11\right)^3=2^5.5^2+200\)
\(\Leftrightarrow\left(7x-11\right)^3=32.25+200=1000\)
\(\Leftrightarrow\left(7x-11\right)^3=10^3\Leftrightarrow7x-11=10\Leftrightarrow7x=21\Leftrightarrow x=3\)
\(3) \)
\(49.7^x=2041\Leftrightarrow7^2.7^x=7^4\Leftrightarrow2+x=4\Leftrightarrow x=2\)
\(4)\)
\(3^x=243\Leftrightarrow3^x=3^5\Leftrightarrow x=5\)
