ANSWER:
[tex]x=\frac{6\ln5-5\ln7}{2\ln7-\ln5}[/tex]
The value of x is equal to -8.49
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]7^{2x+5}=5^{x-6}[/tex]
We solve for x:
[tex]\begin{gathered} (2x+5)\cdot\ln (7)=(x-6)\ln (5) \\ \ln 7\cdot2x+5\ln 7=\ln 5\cdot x-6\ln 5 \\ \ln 7\cdot2x-\ln 5\cdot x=-6\ln 5-5\ln 7 \\ x(2\ln 7-\ln 5)=-6\ln 5-5\ln 7 \\ x=\frac{6\ln 5-5\ln 7}{2\ln 7-\ln 5} \\ x\cong-8.49 \end{gathered}[/tex]
The value of x is equal to -8.49
