Question

ALG II

Ashley 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: x + 1 = log 15/log 3
Step 4: x+1 = 2.708050/1.098612
Step 5: x + 1 = 1.418858
Step 6: x = 0.418858

Answer 1

\(\large\color{black}{ \displaystyle3^{x+1}=15 }\)
like this?

Answer 2

That is not your original equation, is it?

Answer 3

It is.. I must've forgotten the square root arrow.

Answer 4

Wait, what is your original question then?

Answer 5

It's already solved, but I have to find out which step is incorrect.

Answer 6

What is your initial equation that you're solving?

Answer 7

If I don't know the initial question, then I can't help you...

Answer 8

\[3^{^{x+1}}=15\]

Answer 9

\(\large\color{black}{ \displaystyle3^{x+1}=15 }\)
\(\large\color{black}{ \displaystyle3^{x+1}\div 3^{1}=15\div 3^{1} }\)
\(\large\color{black}{ \displaystyle3^{x}=5 }\)
\(\large\color{black}{ \displaystyle\log_3(3^{x})=\log_3(5) }\)
\(\large\color{black}{ \displaystyle x\log_3(3)=\log_3(5) }\)
\(\large\color{black}{ \displaystyle x=\log_3(5)\approx 1.4649735207 }\)

Answer 10

this is one way to do it, but lets check yours...

Answer 11

Step 1: log 3x+1 = log15
Step 2: (x + 1)log 3 = log15
Step 3: x + 1 = log 15/log 3

\(\color{red}{\rm Step~4:}\) x + 1 = log (5•3)/log (3)
\(\color{red}{\rm Step~5:}\) x + 1 = [ log (5) +log(3) ]/log (3)
\(\color{red}{\rm Step~6:}\) x + 1 = log (5)/log (3) + log (3)/log (3)
\(\color{red}{\rm Step~7:}\) x + 1 = log (5)/log (3) + 1
\(\color{red}{\rm Step~8:}\) x = log (5)/log (3)
\(\color{red}{\rm Step~9:}\) x = 1.4649735207

Answer 12

She went wrong at Step 4?

Answer 13

wherever the error was, the error is clearly wrong.

Answer 14

The error is that:
log(3)=0.477

Answer 15

So yes, Step 4 is wrong.