Question

hw unit 15 - logarithmic and exponential equations; applications
question 2 of 35 (1 point) | question attempt: 1 of unlimited
(a) write the equation in exponential form.
(b) solve the equation from part (a).
(c) verify that the solution checks in the original equation.
\\(\log_{2}(3x + 10) = 4\\)
part 1 of 3
(a) the equation in exponential form is \\(2^{4} = 3x + 10\\).
part: 1 / 3
part 2 of 3
(b) the solution set is \\(\\{\quad\\}\\).

Explanation:

Step1: Calculate \(2^4\)

We know that \(2^4 = 2\times2\times2\times2 = 16\). So the equation from part (a) \(2^4 = 3x + 10\) becomes \(16 = 3x + 10\).

Step2: Solve for \(x\)

Subtract 10 from both sides of the equation: \(16 - 10 = 3x + 10 - 10\), which simplifies to \(6 = 3x\). Then divide both sides by 3: \(\frac{6}{3}=\frac{3x}{3}\), so \(x = 2\).

Answer:

\(\{2\}\)