Answer:
The correct option is right-bracket squared 3 squared =x+5
Step-by-step explanation:
The equation is \log _{3}(x+5)=2
Option a: \log _{3}(x+5)=3^{2}
This is not possible because using logarithmic rule, if \log _{a} b=c then b=a^{c}
Hence, option a is not equivalent to \log _{3}(x+5)=2
Option b: \log _{3}(x+5)=2^{3}
This is not possible because using logarithmic rule, if \log _{a} b=c then b=a^{c}
Hence, option b is not equivalent to \log _{3}(x+5)=2
Option c: x+5=3^{2}
This is possible because using logarithmic rule, if \log _{a} b=c then b=a^{c}
Hence, option c is equivalent to \log _{3}(x+5)=2
Option b: x+5=2^{3}
This is not possible because using logarithmic rule, if \log _{a} b=c then b=a^{c}
Hence, option b is not equivalent to \log _{3}(x+5)=2
Thus, the correct option is c: x+5=3^{2}
Hence, the equation x+5=3^{2} is equivalent to \log _{3}(x+5)=2
![\frac{1}{ \frac{343}{3} } \int\limits^7_0 \int\limits^{x^2}_0 {4x\sin(y)} \, dydx = -\frac{3}{343} \int\limits^7_0 {4x\cos(x^2)} \, dx \\ \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B343%7D%7B3%7D%20%7D%20%20%5Cint%5Climits%5E7_0%20%20%5Cint%5Climits%5E%7Bx%5E2%7D_0%20%7B4x%5Csin%28y%29%7D%20%5C%2C%20dydx%20%20%3D%20-%5Cfrac%7B3%7D%7B343%7D%20%20%5Cint%5Climits%5E7_0%20%7B4x%5Ccos%28x%5E2%29%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D-%5Cfrac%7B3%7D%7B343%7D%20%5Cint%5Climits%5E%7B49%7D_0%20%7B2%5Ccos%28t%29%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%20%5Cleft%5B%5Csin%28t%29%5Cright%5D_0%5E%7B49%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%5Csin49)