Let logb 2=2.217 and logb 3=3.417. Find logb 3b
Please walk me through this steo by step.
One of the main rules of logs is this one:
log (AB) = log A + log B , as long as the base is the same in all log expressions.
We have that case here, everything is in terms of base b
so logb (3b) = logb</sub 3 + logb</sub b
= 3.417 + 1 , since logb</sub b = 1
= 4.417
To find logb 3b, we can use the properties of logarithms. In particular, we can use the identity:
logb (mn) = logb m + logb n
Using this identity, we can rewrite logb 3b as:
logb 3b = logb 3 + logb b
Now, we need to find the values of logb 3 and logb b.
We are given that logb 3 = 3.417.
To find logb b, we need to remember that the logarithm of the base itself is always equal to 1. So, logb b = 1.
Now, we can substitute these values into our equation:
logb 3b = logb 3 + logb b
= 3.417 + 1
= 4.417
Therefore, logb 3b is equal to 4.417.