Question

Ciara solved the exponential equation 3x+1 = 15 and her work is shown below. What is the first step she did incorrectly?

Step 1: log 3x+1 = log15
Step 2: (x + 1)log 3 = log15
Step 3: log3 = log 15 over x plus 1
Step 4: 0.477121 = 1.176091 over x plus 1
Step 5: 0.477121(x + 1) = 1.176091
Step 6: x + 1 = 1.176091 over 0.477121
Step 7: x + 1 = 2.464975
Step 8: x = 1.464975

A. Step 1
B. Step 2
C. Step 3
D. Step 4

Answer 1

The step that she  did incorrectly would be step 3. For this we need to isolate the variable x. So, dividing x+1 should not be done because you are limiting the domain which is not main goal here. I hope this answers the question. Have a nice day.

Answer 2

The correct option is C. The first step that Ciara did incorrectly, is step 3.

Explanation:

The given equation is,

`3^(x+1)=15`

The following steps are used to solve the equation.

Taking log both sides,

`log3^(x+1)=log15`

Use the property of logarithm
`loga^b=bloga`.

`(x+1)log3=log15`

`x+1=(log15)/(log3)`

`x+1=(1.176091)/(0.477121)`

`x+1= 2.464975`

`x=1.464975`

Therefore the first and second steps of Ciara are correct but the third step is incorrect. She divides the equation by (x+1) instead of log3.

Therefore option C is correct.