use the properties of logarithms to write the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
In 3sqrt t
ln (3 *t^(1/2))
ln 3 + ln t^(1/2)
ln 3 + (1/2) ln t
How did you do with the Peruvian fish?
To write the expression In 3sqrt t as a sum, difference, or constant multiple of logarithms, we can use the properties of logarithms.
The property we will use is:
log(base a) b^n = n * log(base a) b
We can rewrite the given expression as:
In 3sqrt t = In (t^(1/3))
Now, we can use the property to rewrite this:
In (t^(1/3)) = (1/3) * In t
Therefore, the expression In 3sqrt t can be written as a constant multiple of a logarithm:
In 3sqrt t = (1/3) * In t
To write the expression In 3sqrt t using the properties of logarithms as a sum, difference, or constant multiple of logarithms, we need to understand the properties of logarithms.
The property we will use is the power rule for logarithms, which states that the logarithm of a power of a number is equal to the product of the exponent and the logarithm of the number. In other words:
log base b of (x^a) = a * log base b of x
Now let's apply this property step by step to rewrite the expression In 3sqrt t:
Step 1: Recognize 3√t as (t^(1/3))
So the expression becomes log base b of (t^(1/3))
Step 2: Apply the power rule for logarithms
Using the power rule, we can rewrite the expression as (1/3) * log base b of t.
Therefore, the expression In 3sqrt t can be written as (1/3) * log base b of t.