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

Answer 1

The equation: \(\color{#000000 }{ \displaystyle 3^{x+1}=15 }\)

Step 1: \(\color{#000000 }{ \displaystyle 3^{x+1}=15 }\)

Step 2: \(\color{#000000 }{ \displaystyle \log(3^{x+1})=\log(15) }\)

Step 3: \(\color{#000000 }{ \displaystyle \log(3)=\frac{\log(15)}{x+1} }\)

Step 4: \(\color{#000000 }{ \displaystyle 0.477121 =\frac{1.176091}{ x+1} }\)

Step 5: \(\color{#000000 }{ \displaystyle 0.477121(x+1) =1.176091 }\)

Step 6: \(\color{#000000 }{ \displaystyle x+1 =\frac{1.176091}{ 0.477121} }\)

Step 7: \(\color{#000000 }{ \displaystyle x + 1 = 2.464975 }\)

Step 8: \(\color{#000000 }{ \displaystyle x = 1.464975 }\)

Answer 2

That is the equation and those are the steps.
Am I interpreting the question correctly?

Answer 3

yep

Answer 4

I don't think any of the steps were incorrectly done, however, some steps were a lot of extra work....

Answer 5

my bad,

step 1:
\(\color{#000000 }{ \displaystyle\log(3^{x+1})=\log(15) }\)

step 2:
\(\color{#000000 }{ \displaystyle(x+1)\log(3)=\log(15) }\)

Answer 6

And then all you need is:

\(\color{#000000 }{ \displaystyle x+1=\frac{\log(15)}{\log(3)} }\)

Answer 7

and then you are two steps from the solution.

Answer 8

so im guessing step 3 is incorrect

Answer 9

Yes.

I would rather say that step 3 is a waste.

Answer 10

ok... ty

Answer 11

yw