If log (base b) 3 = 1.099 and
log (base b) 6 = 1.792,
find log (base b) 18 = ???
logb (18)=logb(3*6)=logb3 + logb6
To find log(base b) 18, we can use the properties of logarithms. Specifically, we can use the property that log(base b) of a product is equal to the sum of the logarithms of the individual factors.
Since 18 = 3 * 6, we can write:
log(base b) 18 = log(base b) (3 * 6)
Using the logarithmic property mentioned above, we can rewrite this as:
log(base b) 18 = log(base b) 3 + log(base b) 6
Now we can substitute the given values of log(base b) 3 and log(base b) 6:
log(base b) 18 = 1.099 + 1.792
Evaluating the sum, we get:
log(base b) 18 = 2.891
To find log (base b) 18, we can use the properties of logarithms. One such property is that log (a * b) = log (a) + log (b).
In this case, we are given log (base b) 3 = 1.099 and log (base b) 6 = 1.792. Let's use these values to find log (base b) 18.
We know that 18 = 3 * 6. By applying the property mentioned earlier, we can write:
log (base b) 18 = log (base b) (3 * 6)
Then, using the property log (a * b) = log (a) + log (b), we have:
log (base b) 18 = log (base b) 3 + log (base b) 6
Substituting the given values, we get:
log (base b) 18 = 1.099 + 1.792
Adding the values, we get:
log (base b) 18 = 2.891
Therefore, log (base b) 18 is approximately equal to 2.891.