Question

Use properties of logarithms to expand the logarithmic expression below as much as possible.

log= √ab³/(c⁴)

Answer 1

The expanded form of the given logarithmic expression as much as possible is: log(√ab³/(c⁴)) = (1/2) (log(a) + 3 log(b)) - 4 * log(c)

Step-by-step explanation:

The given logarithmic expression is:

log(√ab³/(c⁴))

To expand this expression, we can use the properties of logarithms. The properties of logarithms state that:

log_b(xy) = log_b(x) + log_b(y)

log_b(x/y) = log_b(x) - log_b(y)

log_b(x^p) = p * log_b(x)

Using these properties, we can expand the given expression step by step.

First, let’s rewrite the expression using the properties of exponents:

log(√ab³/(c⁴)) = log((ab³)^(1/2)) - log(c⁴)

Now, applying the property of logarithms for exponents, we get:

= (1/2) log(ab³) - 4 log(c)

Next, we can further expand the expression using the properties of logarithms for multiplication and division:

= (1/2) (log(a) + 3 log(b)) - 4 * log(c)

So, the expanded form of the given logarithmic expression as much as possible is:

log(√ab³/(c⁴)) = (1/2) (log(a) + 3 log(b)) - 4 * log(c)