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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

Respuesta :

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:

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

Step-by-step explanation:

The given equation is,

[tex]3^{x+1}=15[/tex]

The following steps are used to solve the equation.

Taking log both sides,

[tex]log3^{x+1}=log15[/tex]

Use the property of logarithm [tex]loga^b=bloga[/tex].

[tex](x+1)log3=log15[/tex]

[tex]x+1=\frac{log15}{log3}[/tex]

[tex]x+1=\frac{1.176091}{0.477121}[/tex]

[tex]x+1= 2.464975[/tex]

[tex]x=1.464975[/tex]

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.

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