Question

Keisha is solving the equation 7 to the power of x equals 9. Which equation shows the first step she should take?

Question 4 options:

log 7 to the power of x equals log 9

log 7 to the power of x equals 9

7 x equals log 9

log 7 to the power of x equals ln 9


Mary is solving the equation 2 to the power of n end power minus 3 equals 83. Her first three steps are shown:

Step 1: 2 to the power of n end power minus 3 equals 83
Step 2: 2 to the power of n equals 86
Step 3: ln 2 to the power of n end power equals ln 86

Which equation could be Step 4?

Question 5 options:
n equals ln 86 minus ln 2

ln 2 equals n ln 86

n plus ln 2 equals ln 86

n ln 2 equals ln 86

What is the exact solution of 2 e to the power of x equals 14?

Question 6 options:

ln 7

ln 12

2 ln 14

2 ln 7

Answer 1

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)

Explanation:

Ok,

Question 4: the equation that shows the first step Keisha should take is:

`7^(x)=9`

`log(7^(x) )=log(9)`

`x(log(7))=log(9)` (applying the properties of logarithms)

`x=(log(9))/(log(7)) =1.129`

Solution: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: Her first three steps are:

`2^(n)-3=83`

`2^(n)-3+3=83+3` (adding 3 to both sides)

`2^(n)=86`

`2^(n)-3+3=83+3`

`nln(2)=ln(86)`

Solution: step 4 is:
`nln(2)=ln(86)` (applying the properties of logarithms)

Question 6: The exact solution of 2 e to the power of x equals 14 is:

`2e^(x)=14`

`(2e^(x) )/(2) =(14)/(2)` (dividing both sides by 2)

`e^(x)=7`

`xln(e)=ln7` (ln(e)=1)

`x=ln(7)`

Solution:
`x=ln(7)`