In a school with 300 students, a random sample of 40 students who were asked to pick a favorite sport showed that 24 students like to play basketball the most. What number of students in the whole school can be predicted to prefer basketball? PL I NEED ANSWER RIGHT NOW!
Explanation is in a file
tinylnk.cf/rW5p
i think the amount would be $140.62
[tex]2^{2x+11}=3^{x-31}[/tex]
take the logarithm of both sides (the base of the log doesn't matter):
[tex]\ln2^{2x+11}=\ln3^{x-31}[/tex]
apply the exponent property - this says that [tex]\ln a^b=b\ln a[/tex]:
[tex](2x+11)\ln2=(x-31)\ln3[/tex]
distribute the log terms on both sides:
[tex](2\ln2)x+11\ln2=(\ln3)x-31\ln3[/tex]
group like terms together:
[tex](2\ln2-\ln3)x=-11\ln2-31\ln3[/tex]
divide through both sides by the coefficient on [tex]x[/tex]:
[tex]x=-\dfrac{11\ln2+31\ln3}{2\ln2-\ln3}[/tex]
you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:
[tex]x=-\dfrac{\ln2^{11}+\ln3^{31}}{\ln2^2-\ln3}[/tex]
[tex]x=-\dfrac{\ln2^{11}3^{31}}{\ln\frac43}[/tex]
[tex]x=-\log_{4/3}2^{11}3^{31}[/tex]