Question

section 1.8: logarithmic funct
score: 90/120 answered: 9/12
question 10
solve: \\(\log_{2}(7x + 2) = 2\\),
\\(x = \\)
question help: video
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Explanation:

Step1: Convert log to exponential form

Using the definition of logarithms: if $\log_b(a) = c$, then $b^c = a$. For $\log_2(7x + 2) = 2$, we get $2^2 = 7x + 2$.

Step2: Simplify the equation

Calculate $2^2 = 4$, so the equation becomes $4 = 7x + 2$.

Step3: Solve for x

Subtract 2 from both sides: $4 - 2 = 7x$, so $2 = 7x$. Then divide both sides by 7: $x = \frac{2}{7}$.

Answer:

$\frac{2}{7}$