Answer:
The correct answers are:
Question 4: the first step Keisha should take is: log to the power of x equals log 9.
Question 5: step 4 could be n ln 2 equals ln 86
Question 6: the exact solution is x=ln(7)
Step-by-step explanation:
Ok,
Question 4: the equation that shows the first step Keisha should take is:
[tex]7^{x}=9[/tex]
[tex]log(7^{x} )=log(9)[/tex]
[tex]x(log(7))=log(9)[/tex] (applying the properties of logarithms)
[tex]x=\frac{log(9)}{log(7)} =1.129[/tex]
Solution: the first step Keisha should take is: log to the power of x equals log 9.
Question 5: Her first three steps are:
[tex]2^{n}-3=83[/tex]
[tex]2^{n}-3+3=83+3[/tex] (adding 3 to both sides)
[tex]2^{n}=86[/tex]
[tex]2^{n}-3+3=83+3[/tex]
[tex]nln(2)=ln(86)[/tex]
Solution: step 4 is: [tex]nln(2)=ln(86)[/tex] (applying the properties of logarithms)
Question 6: The exact solution of 2 e to the power of x equals 14 is:
[tex]2e^{x}=14[/tex]
[tex]\frac{2e^{x} }{2} =\frac{14}{2}[/tex] (dividing both sides by 2)
[tex]e^{x}=7[/tex]
[tex]xln(e)=ln7[/tex] (ln(e)=1)
[tex]x=ln(7)[/tex]
Solution: [tex]x=ln(7)[/tex]
