Question

or the exact value of x.
\log_{2}(7x) + \log_{2}(2) = 1

Explanation:

Step1: Apply log addition rule

Using the property \(\log_a(M) + \log_a(N)=\log_a(MN)\), we combine the left - hand side:
\(\log_2(7x)+\log_2(2)=\log_2((7x)\times2)=\log_2(14x)\)
So the equation becomes \(\log_2(14x) = 1\)

Step2: Convert log to exponential form

Recall that if \(\log_a(b)=c\), then \(b = a^c\). For \(a = 2\), \(b=14x\) and \(c = 1\), we have:
\(14x=2^1\)

Step3: Solve for x

Simplify the right - hand side: \(2^1 = 2\). Then we solve the equation \(14x=2\) for \(x\) by dividing both sides by 14:
\(x=\frac{2}{14}=\frac{1}{7}\)

Answer:

\(\frac{1}{7}\)