5.3^x = 8.3¹⁰ - 3.3¹⁰ 

<=> 5.3^x = ( 8-3 ) . 3¹⁰

<=> 5.3^x = 5 .3¹⁰ 

<=>    x = 10 

>< 

\(5.3^x=8.3^{10}-3.3^{10}\)

\(\Rightarrow5.3^x=\left(8-3\right).3^{10}\)

\(\Rightarrow5.3^x=5.3^{10}\)

\(\Rightarrow x=10\)

I have a crazy idea chơi bửn thế. Sao lại chép đáp án của Nguyen Thuy Trinh

13, ta có 25\(\le5^x\le125\)

Hay 5^{2 \(\le\)} 5^{x \(\le\)} 5³

suy ra 2 \(\le\) x \(\le\) 3

Cái này chắc là làm đến đây thôi vì có thể x là phân số hoặc số thập phân thì chịu !!!!

13) \(25\le5^x\le125\\ 5^2\le5^x\le5^3\\ \Rightarrow2\le x\le3\\ \Rightarrow x\in\left\{\varnothing\right\}\)

14,

Ta có :

5.3x^x = 8.3¹⁰ - 3.3¹⁰

5.3^x = 3¹⁰(8-3)

5.3^x = 3¹⁰.5

=>3^x=3¹⁰

=>x=10

Xong !

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lAM THI TUI LAM CHU K THI KHONG

a.\(\frac{11^4.11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5-9^8.7}:\frac{10^5-10^5.3}{10^5.11}\)

=\(\frac{11^4.11^5}{11^4-11^4.11}:\frac{9^8.3-9^8.9}{9^8.5-9^8.7}:\frac{10^5-10^5.3}{10^5.11}\)
=\(\frac{11^4.11^5}{11^4.\left(1-11\right)}:\frac{9^8.\left(3-9\right)}{9^8.\left(5-7\right)}:\frac{10^5.\left(1-3\right)}{10^5.11} \)
=\(\frac{11^4.11^5}{11^4.\left(-10\right)}:\frac{9^8.\left(-6\right)}{9^8.\left(-2\right)}:\frac{10^5.\left(-2\right)}{10^5.11}\)
=\(\frac{11^5}{-10}:3:\frac{-2}{11}\)
=\(\frac{11^5}{-10}.\frac{1}{3}.\frac{-11}{2}\)

Chiều mình làm tiếp cho nha!👋

*** \(\dfrac{15-x}{8}=\dfrac{x-23}{10}\)

\(\Rightarrow10\left(15-x\right)=8\left(x-23\right)\)

\(\Rightarrow150-10x=8x-184\)

\(\Rightarrow150+184=10x+8x\)

\(\Rightarrow18x=334\)

\(\Rightarrow x=\dfrac{167}{9}\)

*** \(\dfrac{1}{2}\left|2x-1\right|-3\dfrac{2}{5}=\left(-\dfrac{1}{2}\right).\left(2015\right)^0\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|-3\dfrac{2}{5}=\left(-\dfrac{1}{2}\right).1\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|-3\dfrac{2}{5}=\left(-\dfrac{1}{2}\right)\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|-3\dfrac{2}{5}=\left(-\dfrac{1}{2}\right)\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|=\left(-\dfrac{1}{2}\right)+3\dfrac{2}{5}\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|=\dfrac{29}{10}\)

\(\Rightarrow\left|2x-1\right|=\dfrac{29}{10}:\dfrac{1}{2}\)

\(\Rightarrow\left|2x-1\right|=\dfrac{29}{5}\)

\(\Rightarrow\left[{}\begin{matrix}2x-1=\dfrac{29}{5}\\2x-1=-\dfrac{29}{5}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=\dfrac{34}{5}\\2x=-\dfrac{24}{5}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{17}{5}\\x=-\dfrac{12}{5}\end{matrix}\right.\)

a.

\(\frac{11^4\times6-11^5}{11^4-11^5}=\frac{11^4\times\left(6-11\right)}{11^4\times\left(1-11\right)}=\frac{-5}{-10}=\frac{1}{2}\)

b.

\(\frac{9^8\times3-3^{18}}{9^8\times5+9^8\times7}=\frac{9^8\times3-\left(3^2\right)^9}{9^8\times\left(5+7\right)}=\frac{9^8\times3-9^9}{9^8\times12}=\frac{9^8\times\left(3-9\right)}{9^8\times12}=-\frac{6}{12}=-\frac{1}{2}\)

c.

\(\frac{10^5-10^5\times3}{10^5\times11}=\frac{10^5\times\left(1-3\right)}{10^5\times11}=-\frac{2}{11}\)

Chúc bạn học tốt

11/2 mink đoán thế,số thập phân thì là 5,5

\(2^{x-1}=3^{y-x}\Rightarrow x-1=y-x=0\Rightarrow\hept{\begin{cases}x=1\\y=1\end{cases}}\)

\(2^{x+1}.3^y=12^x\Rightarrow2^{x+1}.3^y=2^{2x}.3y\Rightarrow\frac{2^{2x}}{2^{x+1}}=\frac{3^y}{3^x}\Rightarrow2^{2x-x-1}=3^{y-x}\)