Question

Use the following equation:
log2x + log2(x – 7) = 3

To solve the equation, first:
Select one:
a. Use the quotient property of logarithms to condense the equation.
b. Use the product property of logarithms to condense the equation.
c. Use the power property of logarithms to condense the equation.
d. Either B or C

Answer 1

b is the answer

Answer 2

\(\normalsize\color{black}{ \log_2x + \log_2(x – 7) = 3}\) use `log(a)+log(b)=log(a×b)`

\(\normalsize\color{black}{ \log_2x\times (x – 7) = 3}\) simplify inside the log.

\(\normalsize\color{black}{ \log_2~x^2 – 7x = 3}\)

\(\normalsize\color{black}{ \log_2~x^2 – 7x = 3\log_22}\)


\(\normalsize\color{black}{ \log_2~x^2 – 7x = \log_22^3}\)

\(\normalsize\color{black}{ \log_2~x^2 – 7x = \log_28}\)

\(\normalsize\color{black}{ x^2 – 7x = 8}\)

\(\normalsize\color{black}{ x^2 – 7x -8= 0}\)

\(\normalsize\color{black}{ (x-8)(x+1)= 0}\)

\(\normalsize\color{black}{ x=8,~~-1}\)

Answer 3

I was to long, I should have said 3=3log(2)2 → log(2)9
then subtracted that log from both sides, then used the product and division of log rules.