Understand Equation: Understand the given logarithmic equation. The equation log 30 = log(-3b - 5) implies that the logarithmic expressions on both sides of the equation are equal. Therefore, the arguments of the logarithms must be equal.Set Arguments Equal: Set the arguments of the logarithms equal to each other. Since the logs are equal and have the same base, we can set their arguments equal to each other: 30 = -3b - 5Solve for b: Solve for b. To find the value of b, we need to isolate b on one side of the equation. We will add 5 to both sides and then divide by -3. 30 + 5 = -3b - 5 + 5 35 = -3b b = -35 / -3 b = 35 / 3

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$92$ ) $\log 30=\log (-3 b-5)$

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Precalculus

Product property of logarithms

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\log 30=\log (-3 b-5)

Understand Equation: Understand the given logarithmic equation. $\newline$ The equation $\log 30 = \log(-3b - 5)$ implies that the logarithmic expressions on both sides of the equation are equal. Therefore, the arguments of the logarithms must be equal.
Set Arguments Equal: Set the arguments of the logarithms equal to each other. $\newline$ Since the logs are equal and have the same base, we can set their arguments equal to each other: $\newline$ $30 = -3b - 5$
Solve for b: Solve for b. $\newline$ To find the value of $b$ , we need to isolate $b$ on one side of the equation. We will add $5$ to both sides and then divide by $-3$ . $\newline$ $30 + 5 = -3b - 5 + 5$ $\newline$ $35 = -3b$ $\newline$ $b = -35 / -3$ $\newline$ $b = 35 / 3$