ln24 - ln6
To subtract the natural logarithm of 6 (ln6) from the natural logarithm of 24 (ln24), subtract the values inside the parentheses.
ln24 - ln6 = ln(24/6)
Simplifying further,
ln24 - ln6 = ln(4)
Therefore, ln24 - ln6 = ln(4)
To find the value of ln24 - ln6, we can use the properties of logarithms.
The property we can use in this case is:
ln(a) - ln(b) = ln(a/b)
Using this property, we can rewrite ln24 - ln6 as ln(24/6).
Simplifying further, 24/6 is equal to 4. Therefore, ln(24/6) = ln4.
Now, to find the value of ln4, we can use the fact that ln4 is the natural logarithm of the number e raised to what power gives us 4.
In other words, we need to solve the equation:
e^x = 4, where x is the unknown power.
To solve this equation, we need to take the natural logarithm of both sides:
ln(e^x) = ln(4)
Applying the property ln(e^x) = x, we obtain:
x = ln(4)
Using a calculator, we can evaluate ln(4) ≈ 1.386.
Therefore, ln24 - ln6 ≈ 1.386
ln (24/6) using the law of logs or lns where subtraction becomes division.
so you have ln 4