Bài 6: Lũy thừa của một số hữu tỉ (tiếp theo...)

\(x^{-n}=\dfrac{1}{x^n}\Leftrightarrow x^{-n}\cdot x^n=1\)

Thấy: \(x^{-n};x^n\) là 2 số đối nhau

Suy ra \(x^{-n}\cdot x^n=1\)

a. 2^x = 8 ; b. 5^x = 25 ; c. 3^x : 3⁵ = 9 d. \(\dfrac{16}{2^x}=2\) ; e. 8^x : 2^x = 4 ; f. 2^x . 3^x = 36 ; g. \(\dfrac{\left(-3\right)^n}{81}=-27\)

2^x = 2³ 5^x = 5² 3^x : 3⁵ = 3^{2 \(\dfrac{2^4}{2^x}=1\)} ( 2³)^x : 2^x = 2² 6^x = 6² \(\dfrac{\left(-3\right)^n}{\left(-3\right)^4}=\left(-3\right)^3\)

x = 3 x = 3 3^x = 3² . 3^{5 \(2^{4-x}=2^1\)} 2^3x : 2^x = 2² x = 2 \(\left(-3\right)^n=\left(-3\right)^3.\left(-3\right)^4\)

3^x = 3^{7 \(\Rightarrow4-x=1\)} 2^{3x - x} = 2² \(\left(-3\right)^n=\left(-7\right)^7\)

=>X = 7 x = 4 - 1 2^2x = 2² => n = 7

x = 3 2x = 2

x = 2 : 2

x = 1

a: \(\Leftrightarrow2^x\cdot\dfrac{1}{2}+2^x\cdot2=2^{10}\left(2^2+1\right)\)

\(\Leftrightarrow2^x=2^{10}\cdot5:\dfrac{5}{2}=2^{10}\cdot5\cdot\dfrac{2}{5}=2^{11}\)

=>x=11

b: \(\Leftrightarrow3^x\cdot\dfrac{1}{3}+3^x\cdot9=3^{13}\cdot28\)

\(\Leftrightarrow3^x=3^{13}\cdot28:\dfrac{28}{3}=3^{14}\)

hay x=14

\(\text{a) }\dfrac{\left(-6\right)^6}{216}=\dfrac{6^6}{216}=\dfrac{6^6}{6^3}=6^3=216\)

\(\text{b) }\dfrac{64}{\left(-4\right)^5}=-\dfrac{64}{4^5}=-\dfrac{4^3}{4^5}=-\dfrac{1}{4^2}=-\dfrac{1}{16}\)

\(\text{c) }\dfrac{900}{\left(-30\right)^3}=-\dfrac{900}{30^3}=-\dfrac{30^2}{30^3}=-\dfrac{1}{30}\)

\(\text{d) }\dfrac{225}{15^3}=\dfrac{15^2}{15^3}=\dfrac{1}{15}\)

Đề nghị bạn trình bày câu hỏi rõ ràng hơn nữa

\(5^{x^2+x-6}=1\)

\(\Rightarrow5^{x^2+x-6}=5^0\)

Vì \(5\ne-1;5\ne0;5\ne1\) nên

\(x^2+x-6=0\Rightarrow x^2-2x+3x-6=0\)

\(\Rightarrow x.\left(x-3\right)+3.\left(x-2\right)=0\)

\(\Rightarrow\left(x-2\right)\left(x+3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)

Vậy..........

Chúc bạn học tốt!!!

\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\dfrac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2.6}{3.5}=\dfrac{12}{15}=\dfrac{4}{5}\)

Chúc bạn học tốt!!!

a, \(5^x+5^{x+1}+5^{x-2}=151\)

\(\Rightarrow5^x.\left(1+5+5^{-2}\right)=151\)

\(\Rightarrow5^x.6,04=151\Rightarrow5^x=25=5^2\)

Vì \(5\ne-1;5\ne0;5\ne1\) nên \(x=2\)

b, \(5^{x-1}+5^{x-2}+5^{x-3}=155\)

\(\Rightarrow5^x.\left(5^{-1}+5^{-2}+5^{-3}\right)=155\)

\(\Rightarrow5^x.0,248=155\Rightarrow5^x=625=5^4\)

Vì \(5\ne-1;5\ne0;5\ne1\) nên \(x=4\)

\(•5^x+5^{x+1}+5^{x-2}=151\\ 5^x\left(1+5+\dfrac{1}{25}\right)=151\\ 5^x=25\\ \Rightarrow x=2\)

\(•5^{x-1}+5^{x-2}+5^{x-3}=155\\ 5^x.\left(\dfrac{1}{5}+\dfrac{1}{25}+\dfrac{1}{125}\right)=155\\ 5^x=625\\ \Rightarrow x=4\)

\(•5^{2+x}+5^{3+x}=750\\ 5^x\left(25+125\right)=750\\ 5^x=5\\ \Rightarrow x=1\)

\(x^2-\dfrac{1}{10}=\dfrac{23}{90}\)

\(x^2-\dfrac{9}{90}=\dfrac{23}{90}\)

\(x^2=\dfrac{16}{45}\)

\(\Leftrightarrow x=\sqrt{\dfrac{16}{45}}\)

\(\Leftrightarrow x=-\sqrt{\dfrac{16}{45}}\)

=15625

45^10*5^20/75^15

=(3^2*5)^10*5^20/(3*5^2)^15

=3^20*5^10*5^20/3^15*5^30

=3^20*5^30/3^15*5^30

=3^5=243