Given logb3 = 0.792 and logb5 = 1.161. If possible, use the properties of logarithms to calculate values for the following show your work
logb 1/3
log 1 is 0 for any base at all
so
logb (1/3) = 0 - .792
To calculate logb(1/3), we can use the property of logarithms that states logb(a/b) = logb(a) - logb(b).
In this case, we have logb(1/3) = logb(1) - logb(3).
Now, we know that logb(1) is equal to 0 because any logarithm of 1 to any base is always 0.
So, logb(1/3) = 0 - logb(3).
To find logb(3), we need to use the properties of logarithms again. We can rewrite logb(3) as logb(3^1) because any number raised to the power of 1 equals itself.
Therefore, logb(3) = 1 * logb(3).
Using the given values, logb3 = 0.792.
Now, we can substitute this value into the equation:
logb(1/3) = 0 - logb(3) = 0 - 1 * logb(3) = 0 - 1 * 0.792 = -0.792.
Therefore, logb(1/3) is approximately equal to -0.792.