logb3=1.099
logb8=2.079
find logb216
i am just lost on what to do
8*what=216
what=27
8*27=216
8*3^3=216
take the logb both sides
logb8 + 3logb3=log216
2.079+3*1.099=?
To find logb216, you can use the logarithmic property of exponents, which states that logb(x^a) = a * logb(x).
Since 216 is equal to 6^3 (6 * 6 * 6) and logb3 = 1.099, we can rewrite logb216 as logb(6^3).
Using the logarithmic property, we can rewrite this expression as 3 * logb6.
However, we do not know the value of logb6. We need to find that first.
To find logb6, we can think of 6 as 8/3. Therefore, we can rewrite logb6 as logb(8/3).
Using the logarithmic property, this expression can be written as logb8 - logb3.
We know that logb3 = 1.099 and logb8 = 2.079.
Substituting these values, we have logb6 = logb8 - logb3 = 2.079 - 1.099 = 0.98.
Now, we can substitute the value of logb6 into our original expression to find logb216:
logb216 = 3 * logb6 = 3 * 0.98 = 2.94.
Therefore, logb216 is approximately equal to 2.94.