Question

Express V in terms of other quantities in the following:

log V + log 3 = log π + 2 log r + log h

Answer 1

We are given:

log V + log 3 = log π + 2 log r + log h

Step 1: Combine the logarithms

We can use the logarithmic property log a + log b = log(ab).

On the left side:

log V + log 3 = log(V × 3) = log(3V)

On the right side:

2 log r = log r²  (using the logarithmic property a log b = log(b^a))

So:

log π + log r² + log h = log(π × r² × h)

Now the equation becomes:

log(3V) = log(π × r² × h)

Step 2: Equate the arguments of the logarithms

Since log a = log b implies a = b, we have:

3V = πr²h

Step 3: Solve for V

`V = (πr^2h)/3`