Answer:
2) x = 0.3281
3) x = 1.31
Step-by-step explanation:
2. We have been given the equation [tex]10^{6x}=93[/tex]
Take logarithm both sides
[tex]\log(10^{6x})=\log93[/tex]
Use the power rule of logarithm: [tex]\log x^m=m\log x[/tex]
[tex]6x\log10=\log93[/tex]
The value of log10 is 1. Hence, we have
[tex]6x=\log93[/tex]
Divide both sides by 6
[tex]x=\frac{1}{6}\cdot\log93\\\\x=0.3281[/tex]
Thus the value of x is 0.3281
3)
We have to solve the equation [tex]5.5^{3x}=805[/tex] by graphing calculator.
We graph the below two equations in the same xy- plane and the x- coordinate of the intersection point would be the solution to the graph.
[tex]y=5.5^{3x}\\\\y=805[/tex]
Please see the attache graph. The intersection point is (1.308,805)
The x-coordinate is 1.308. Hence, the solution is x = 1.308.
Rounded to the nearest hundredth, we have
x = 1.31
