Condense the logarithm
log a +3 log c
log a + 3 log c = log a + log c^3 = log(ac^3)
To condense the logarithm `log a + 3 log c`, we can use the properties of logarithms:
1. The sum rule: `log a + log b = log (a * b)`
2. The power rule: `n log a = log (a^n)`
Using these properties, we can rewrite the expression:
`log a + 3 log c = log a + log c^3` (Applying the power rule)
`= log (a * c^3)` (Applying the sum rule)
Therefore, the condensed form of `log a + 3 log c` is `log (a * c^3)`.
To condense the given expression, we can use the properties of logarithms. One of the properties states that the sum of logarithms of the same base is equal to the logarithm of their product.
So, we can rewrite the expression as:
log a + 3 log c = log a + log c^3
Applying another property of logarithms, which states that the sum of logarithms is equal to the logarithm of their product, we can further simplify it.
log a + log c^3 = log (a * c^3)
Thus, the condensed form of the expression is: log (a * c^3)