Question

what is the solution of \\(\log(2t + 4) = \log(14 - 3t)\\)? \\(-18\\) \\(10\\) \\(-2\\) \\(2\\)

Explanation:

Step1: Use the property of logarithms (if $\log_a M = \log_a N$, then $M = N$)

Since $\log(2t + 4) = \log(14 - 3t)$, we can set the arguments equal: $2t + 4 = 14 - 3t$

Step2: Solve for $t$

Add $3t$ to both sides: $2t + 3t + 4 = 14$
Simplify: $5t + 4 = 14$
Subtract 4 from both sides: $5t = 14 - 4$
Simplify: $5t = 10$
Divide both sides by 5: $t = \frac{10}{5}$
Simplify: $t = 2$

Answer:

2