Questions: log(a+b) = log(ab)

Transcript text: $\log (a+b)=\log (a b)$

Solution

Solution Steps

To solve the equation $\log (a+b) = \log (ab)$, we can use the property of logarithms that states if $\log(x) = \log(y)$, then $x = y$. Therefore, we can set the arguments of the logarithms equal to each other: $a + b = ab$. We can then rearrange this equation to solve for one of the variables in terms of the other.

Step 1: Set Up the Equation

We start with the equation derived from the logarithmic property: \[ \log(a + b) = \log(ab) \implies a + b = ab \]

Step 2: Rearrange the Equation

Rearranging the equation gives us: \[ ab - a - b = 0 \] This can be rewritten as: \[ a + b - ab = 0 \]

Step 3: Solve for $a$

To solve for $a$ in terms of $b$, we can rearrange the equation: \[ a = \frac{b}{b - 1} \]

Final Answer

Thus, the solution for $a$ in terms of $b$ is: \[ \boxed{a = \frac{b}{b - 1}} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >