Question

\(\text{Tìm x }\)

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)

Các bn giúp mik vs

Answer 1

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)

\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2^x\)

\(\Rightarrow\frac{4^6}{3^6}.\frac{6^6}{2^6}=2^x\)

\(\Rightarrow\frac{4^6.6^6}{3^6.2^6}=2^x\)

\(\Rightarrow\frac{\left(4.6\right)^6}{\left(3.2\right)^6}=2^x\)

\(\Rightarrow\frac{24^6}{6^6}=2^x\)

\(\Rightarrow4^6=2^x\)

\(\Rightarrow\left(2^2\right)^6=2^x\)

\(\Rightarrow2^{2.6}=2^x\)

\(\Rightarrow2^{12}=2^x\)

\(\Rightarrow x=12\)

Answer 2

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x.\)

\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2^x\)\(\Rightarrow\frac{4^6.6^6}{3^6.2^6}=2^x\)

\(\Rightarrow\frac{2^6.2^6.2^6.3^6}{3^6.2^6}=2^x\)\(\Rightarrow2^6.2^6=2^x\)

\(\Rightarrow2^{12}=2^x\Leftrightarrow x=12\)