Question

[Huỳnh Văn Thiện]

Giải phương trình:

\(2^x+2^{x-1}+2^{x-2}=3^x+3^{x-1}+3^{x-2}\)

Answer 1

[Akai Haruma]

Lời giải:

Ta có:

\(2^{x}+2^{x-1}+2^{x-2}=3^x+3^{x-1}+3^{x-2}\)

\(\Leftrightarrow 2^{x-2}(2^2+2+1)=3^{x-2}(3^2+3+1)\)

\(\Leftrightarrow 2^{x-2}.7=3^{x-2}.13\)

\(\Leftrightarrow \frac{2^{x-2}}{3^{x-2}}=\frac{13}{7}\)

\(\Leftrightarrow \left(\frac{2}{3}\right)^{x-2}=\frac{13}{7}\)

\(\Leftrightarrow x-2=\log_{\frac{2}{3}}\frac{13}{7}\)

\(\Leftrightarrow x=2+\log_{\frac{2}{3}}\frac{13}{7}=\log_{\frac{2}{3}}\frac{4}{9}+\log_{\frac{2}{3}}\frac{13}{7}=\log_{\frac{2}{3}}\frac{52}{63}\)

Vậy \(x=\log_{\frac{2}{3}}\frac{52}{63}\)

Answer 2

[kill one]

Đáp án x=log_(2/3)(52/63)