Question

2. Solve 10^6x = 93. Round to the nearest ten-thousandth.

11.8109
1.0986
13.3801
0.3281

3. Use a graphing calculator. Solve 5.5^3x = 805 by graphing. Round to the nearest hundredth.

2.91
3.92
1.31
0.97

Answer 1

2) x = 0.3281

3) x = 1.31

Explanation:

2. We have been given the equation
`10^(6x)=93`

Take logarithm both sides

`\log(10^(6x))=\log93`

Use the power rule of logarithm:
`\log x^m=m\log x`

`6x\log10=\log93`

The value of log10 is 1. Hence, we have

`6x=\log93`

Divide both sides by 6

`x=(1)/(6)\cdot\log93\\\\x=0.3281`

Thus the value of x is 0.3281

3)

We have to solve the equation
`5.5^(3x)=805` 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.

`y=5.5^(3x)\\\\y=805`

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

Answer 2

Solve 10^6x = 93. Round to the nearest ten-thousandth.
0.3281

3. Use a graphing calculator. Solve 5.5^3x = 805 by graphing. Round to the nearest hundredth.

1.31

Hope this helps. Have a nice day. Feel free to ask more questions. Thank you.