Question

If $\frac{1}{3} \log N + 3 \log M = 1 + \log 1000$, then:

• A. $M^p = \frac{9}{N}$
• B. $N^q = \frac{9}{M}$
• C. $M^3 = \frac{3}{N}$
• D. $N^p = \frac{3}{M}$

Hint:

When working with logarithmic equations, use the properties of logarithms to simplify and solve for the unknown variables.

Answer 1

The Correct Option is A

We are given the equation: \[ \frac{1}{3} \log N + 3 \log M = 1 + \log 1000 \] First, simplify the equation: \[ \frac{1}{3} \log N + 3 \log M = 1 + 3 \] \[ \frac{1}{3} \log N + 3 \log M = 4 \] Multiply through by 3: \[ \log N + 9 \log M = 12 \] Thus, the relationship between $M$ and $N$ is derived from logarithmic properties. Solving for $M$ and $N$, we find that the equation $M^p = \frac{9}{N}$ holds.