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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

1 Answer

4 votes

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)

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)

User Merrill Cook
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