Solve Log Equation: log7x + log(x+1) - log7 = log2x - logx

Logarithms are only defined for positive arguments. When you have $\log(x)$ or $\log(7x)$, the value inside must be greater than zero for the logarithm to exist!

Use these key properties:

• $\log a + \log b = \log(ab)$
• $\log a - \log b = \log(\frac{a}{b})$

Apply them step by step to simplify both sides.

Test each solution individually against the original domain restrictions. Only solutions that make all logarithmic arguments positive are valid answers.

Yes! Once you have $\log A = \log B$, you can conclude that A = B. This gives you a simpler equation without logarithms to solve.

We need both conditions because we have multiple logarithmic terms. Since $\log(7x)$ requires x > 0 and $\log(x+1)$ requires x > -1, we take the stricter condition: x > 0.